5.5 Operations with Radical Expressions

Multiple Choice

Simplify each sum or difference.

• $$9\sqrt{5}$$

• $$15\sqrt{3}$$

• $$-9\sqrt{5}$$

• $$9\sqrt{0}$$

Multiple Choice

Simplify completely.

• 2√3

• -8√3

• 2√6

• -8√6

Multiple Choice

Simplify $$\sqrt{36ab^4c^5}$$  

• $$6b^2c^2\sqrt{ac}$$  

• $$6ab^2c^2$$  

• $$6b^2c^2$$  

• $$6abc\sqrt{c}$$  

Multiple Choice

Which two terms are like radicals?

• $$\sqrt{3}\ and\ \sqrt{9}$$

• $$\sqrt{8}\ and\ \sqrt{2}$$

• $$\sqrt{8}\ and\ \sqrt{4}$$

• $$\sqrt{8}\ and\ \sqrt{3}$$

Multiple Choice

Simplify the expression

• 49

• 7

• √98/√2

• It's already simplified

Multiple Choice

Simplify  $$2\sqrt{5}-7\sqrt{5}-5\sqrt{5}$$  

• $$4\sqrt{5}$$  

• $$14\sqrt{5}$$  

• $$-10\sqrt{5}$$  

• $$0$$  

Multiple Choice

Simplify each sum or difference.

• $$-9\sqrt{1}$$

• $$15\sqrt{2}$$

• $$-3\sqrt{2}$$

• $$2\sqrt{3}$$

Multiple Choice

Simplify $$2\sqrt{45}+4\sqrt{20}$$  

• $$6\sqrt{65}$$  

• $$34\sqrt{5}$$  

• $$14\sqrt{5}$$  

• $$10\sqrt{5}$$  

Multiple Choice

Simplify the expression

• 100√2

• 5√160

• 20√10

• It's already simplified

Multiple Choice

Simplify  $$2\sqrt{32}+3\sqrt{50}-3\sqrt{18}$$  

• $$14\sqrt{2}$$  

• $$4\sqrt{8}+6\sqrt{2}$$  

• $$12\sqrt{2}$$  

• $$32\sqrt{2}$$  

Multiple Choice

Add $$\sqrt{45}+\sqrt{125}$$  

• $$34\sqrt{5}$$  

• $$\sqrt{170}$$  

• $$8\sqrt{5}$$  

• can't add

Multiple Choice

Simplify $$5\sqrt{8}+3\sqrt{20}-\sqrt{32}$$  

• $$10\sqrt{2}+6\sqrt{5}-2\sqrt{8}$$  

• $$6\sqrt{5}+14\sqrt{2}$$  

• $$12\sqrt{10}$$  

• $$6\sqrt{2}+6\sqrt{5}$$  

Multiple Choice

Simplify the expression

• 45/2

• (3√5)/4

• (3√5)/2

• It's already simplified

Multiple Choice

Simplify  $$3\sqrt{10}+\sqrt{75}-2\sqrt{40}-4\sqrt{12}$$  

• $$7\sqrt{10}-3\sqrt{3}$$  

• $$-\sqrt{10}-3\sqrt{3}$$  

• $$-\sqrt{10}+13\sqrt{3}$$  

• $$-5\sqrt{10}+9\sqrt{3}$$  

Multiple Choice

Simplify $$5\sqrt{2x}\times3\sqrt{8x}$$  

• $$60x$$  

• $$15\sqrt{40x^2}$$  

• $$8\sqrt{40x^2}$$  

• $$15\sqrt{16x}$$  

Multiple Choice

Simplify $$\sqrt{5}\left(5\sqrt{2}-4\sqrt{8}\right)$$  

• $$5\sqrt{5}-4\sqrt{40}$$  

• $$-11\sqrt{10}$$  

• $$13\sqrt{10}$$  

• $$-3\sqrt{10}$$  

Multiple Choice

Simplify the expression

• 6a⁵b³√3b

• 2a⁵b³√54b

• 3a⁵b³

• 6√2a¹⁰b⁷

Multiple Choice

Simplify  $$\left(5-\sqrt{15}\right)^2$$  

• $$40-10\sqrt{15}$$  

• $$10$$  

• $$40$$  

• $$25+\sqrt{15}$$  

Multiple Choice

Simplify $$\sqrt{18x^3}-\sqrt{32x^3}$$  

• $$-x\sqrt{2x}$$  

• $$-x\sqrt{2}$$  

• $$-x\sqrt{2x^2}$$  

• $$-7x^2\sqrt{x}$$  

Multiple Choice

Simplify  $$\left(\sqrt{8}+\sqrt{12}\right)\left(\sqrt{48}+\sqrt{18}\right)$$  

• $$5\sqrt{2}+6\sqrt{3}$$  

• $$\sqrt{384}+36+\sqrt{216}$$  

• $$36+14\sqrt{6}$$  

• $$72+14\sqrt{12}$$  

Multiple Choice

Rationalize the denominator.

$$\frac{4}{\sqrt{5}}$$  

• $$\frac{4\sqrt{5}}{5}$$  

• $$\frac{\sqrt{5}}{4}$$  

• $$\frac{\sqrt{6}}{3}$$  

• $$\frac{5\sqrt{2}}{2}$$  

Multiple Choice

Simplify   $$\left(4\sqrt{3}-2\sqrt{5}\right)\left(3\sqrt{10}+5\sqrt{6}\right)$$  

• $$2\sqrt{30}+30\sqrt{2}$$  

• $$2\sqrt{30}+20\sqrt{18}-6\sqrt{50}$$  

• $$22\sqrt{30}+90\sqrt{2}$$  

• $$22\sqrt{30}+30\sqrt{2}$$  

Multiple Choice

Simplify completely.

• 3√8
• 2
• 2√2
• -16

Multiple Choice

A rectangle is  $$5\sqrt{7}+2\sqrt{3}$$  meters long and  $$6\sqrt{7}-3\sqrt{3}$$  meters wide.  Find the PERIMETER of the rectangle in simplest form.

• $$11\sqrt{7}-\sqrt{3}\ \ square\ meters$$  

• $$11\sqrt{7}-\sqrt{3}\ \ meters$$  

• $$22\sqrt{7}-2\sqrt{3}\ \ \ \ square\ meters\$$  

• $$22\sqrt{7}-2\sqrt{3}\ meters$$  

Multiple Choice

Rationalize the denominator:
$$\frac{2\sqrt{8}}{\sqrt{12}}$$  

• $$\frac{\sqrt{96}}{6}$$  

• $$\frac{2\sqrt{6}}{3}$$  

• $$\frac{2\sqrt{96}}{12}$$  

• $$\frac{4\sqrt{2}}{2\sqrt{3}}$$  

Multiple Choice

A rectangle is $$5\sqrt{7}+2\sqrt{3}$$ meters long and  $$6\sqrt{7}-3\sqrt{3}$$  meters wide.  Find the AREA of the rectangle in simplest form.

• $$228-3\sqrt{21}square\ meters$$  

• $$192-3\sqrt{21}square\ meters$$  

• $$192+27\sqrt{21}square\ meters$$  

• $$228+27\sqrt{21}square\ meters$$  

Multiple Choice

Simplify $$\sqrt{7}\left(\sqrt{175}+\sqrt{35}\right)$$  

• $$35+49\sqrt{5}$$  

• $$1225+7\sqrt{5}$$  

• $$35+7\sqrt{5}$$  

• $$70$$  

Multiple Choice

Rationalize the denominator.
$$\frac{5}{6\sqrt{2}}$$

• $$\frac{5\sqrt{2}}{6\sqrt{4}}$$  

• $$\frac{5\sqrt{2}}{12}$$  

• $$\frac{30\sqrt{2}}{24}$$  

• $$\frac{\sqrt{10}}{5}$$  

Multiple Choice

Simplify:

• 6x²
• 18x²

Multiple Choice

Rationalize the denominator. 
$$\frac{\sqrt{3xy^2}}{\sqrt{5xy^3}}$$  

• $$\frac{\sqrt{15y}}{5y}$$  

• $$\frac{3\sqrt{5y}}{5y}$$  

• $$\frac{\sqrt{5y}}{5y}$$  

• $$\frac{\sqrt{15y}}{y}$$  

Multiple Choice

Simplify $$\left(\sqrt{x}-19\right)^2$$  

• $$x-361$$  

• $$x+361$$  

• $$x-38\sqrt{x}+361$$  

• $$x+38\sqrt{x}+361$$  

Multiple Choice

• 11√5
• 11√10
• 5√5
• 12√10

Multiple Choice

Simplify each sum or difference.

• $$48\sqrt{3}$$

• $$47\sqrt{2}$$

• $$42\sqrt{7}$$

• $$9\sqrt{140}$$

Multiple Choice

• -5√1
• 8√2 + 13√3
• 21√5
• 20√5

Multiple Choice

Simplify $$\left(\sqrt{5}+7\right)\left(\sqrt{6}+2\right)$$  

• $$\sqrt{30}+2\sqrt{5}+7\sqrt{6}+14$$  

• $$\sqrt{30}+9\sqrt{6}+14$$  

• $$\times10\sqrt{30}+14$$  

• $$\sqrt{30}+14$$  

Multiple Choice

Simplify:

• 1/5

• 20/100

• 2/10

• 1/√25

Multiple Choice

Simplify:

• $$2x\sqrt{14x}$$

• $$4x\sqrt{14x}$$

• $$2x\sqrt{14x^3}$$

• $$4x\sqrt{14x^3}$$

Multiple Choice

$$-3\sqrt{8}+3\sqrt{18}$$  

• $$-3\sqrt{2}$$  

• $$6\sqrt{2}$$  

• $$15\sqrt{2}$$  

• $$3\sqrt{2}$$  

Multiple Choice

Simplify $$\left(\sqrt{10}+3\right)\left(\sqrt{10}-3\right)$$  

• $$1$$  

• $$7$$  

• $$19$$  

• $$10-2\sqrt{3}$$  

Multiple Choice

$$5\sqrt{3}+\sqrt{12}$$  

• $$7\sqrt{3}$$  

• $$9\sqrt{3}$$  

• $$5\sqrt{15}$$  

• $$6\sqrt{3}$$  

Multiple Choice

Simplify completely.

• -4
• 24
• 5√6
• -5√6

Multiple Choice

$$10\sqrt{6}+2\sqrt{6}$$  

• $$8\sqrt{6}$$  

• $$8\sqrt{12}$$  

• $$12\sqrt{6}$$  

• $$12\sqrt{12}$$  

Multiple Choice

Simplify $$\sqrt{48x^{4\ }}+\sqrt{27x^{4\ }}$$  

• $$\sqrt{75x^4}$$  

• $$\sqrt{75x^8}$$  

• $$7x^2\sqrt{3}$$  

• $$7x\sqrt{3x}$$  

Multiple Choice

$$2\sqrt{3}\left(\sqrt{6}-\sqrt{3}\right)$$

• $$6\sqrt{2}-6$$  

• $$3\sqrt{2}+3$$  

• $$6-\sqrt{3}$$  

• $$\sqrt{3}-\sqrt{2}$$  

Multiple Choice

Simplify:

• $$4\sqrt{30}$$

• $$\sqrt{4}\sqrt{30}$$

• $$\sqrt{2}\sqrt{30}$$

• $$2\sqrt{30}$$

Multiple Choice

$$2\sqrt{3}+2\sqrt{5}-\sqrt{5}+4\sqrt{5}+\sqrt{3}$$

• $$6\sqrt{5}+3\sqrt{3}$$  

• $$5\sqrt{5}+3\sqrt{3}$$  

• $$6\sqrt{5}$$  

• $$6\sqrt{3}$$  

Multiple Choice

Simplify $$\frac{\sqrt{45}}{10}+\frac{7\sqrt{5}}{10}$$  

• $$10\sqrt{5}$$  

• $$\sqrt{5}$$  

• $$\frac{7\sqrt{50}}{10}$$  

• can't simplify

Multiple Choice

Simplify.
(x³ ⋅ y⁴ ⋅ z)³ ⋅ (x⁵ ⋅ y ⋅ z³)²

• x¹⁹y¹²z⁹
• x¹⁹ y¹⁴z⁹
• x¹³y¹⁰z⁹
• x²³y⁴²z¹¹

Multiple Choice

Simplify each sum or difference.

• $$-4\sqrt{3}$$

• $$-7\sqrt{4}$$

• $$-3\sqrt{7}$$

• $$-9\sqrt{2}$$

Multiple Choice

Simplify the expression:  $$\left(\frac{a^3}{2b^5}\right)^4$$  

• $$\frac{a^{12}}{2b^{20}}$$  

• $$\frac{a^7}{2b^9}$$  

• $$\frac{a^{12}}{16b^{20}}$$  

• $$\frac{a^7}{16b^9}$$  

Multiple Choice

Simplify $$\frac{\sqrt{99}}{5x}-\sqrt{\frac{44}{x^2}}$$  

• $$\frac{\sqrt{11}}{5x^2}$$  

• $$\frac{\sqrt{55}}{5x^2}$$  

• $$-\frac{7\sqrt{11}}{5x}$$  

• $$\frac{\sqrt{11}}{5x}$$  

Multiple Choice

Simplify the expression completely.

$$\frac{2x^0y^2}{-yx^{-2}\cdot\left(2xy^0\right)^4}$$  

• $$-8yx^2$$  

• $$8y^2x^{-2}$$  

• $$-\frac{8x^2}{y}$$  

• $$-\frac{y}{8x^2}$$  

Multiple Choice

Simplify the expression

• 49

• 7

• √98/√2

• It's already simplified

Multiple Choice

Simplify the expression completely.

$$\frac{n^4m^2}{\left(-m^{-4}\right)^{-3}}$$  

• $$-\frac{n^4}{m^{10}}$$  

• $$m^{-10}n^{-4}$$  

• $$-\frac{m^{10}}{n^4}$$  

• $$-\frac{1}{m^{10}n^4}$$  

Multiple Choice

Simplify completely.

• -12√5 - 2√6
• -7√6
• -7√19
• simplest form

Multiple Choice

Simplify the expression completely.

$$\frac{\left(-2x^3y^{-3}\right)^2}{\left(-x^{-4}y^0\cdot-2x^4\right)^2}$$  

• $$-\frac{x^6}{y^6}$$  

• $$\frac{x^6}{y^6}$$  

• $$undefined$$  

• $$-\frac{2}{x^6y^7}$$  

Multiple Choice

Add $$\sqrt{45}+\sqrt{125}$$  

• $$34\sqrt{5}$$  

• $$\sqrt{170}$$  

• $$8\sqrt{5}$$  

• can't add

Multiple Choice

Simplify the expression completely.

$$\frac{2x^{-2}y^2}{\left(-2y\cdot-2y^2\right)^4}$$  

• $$\frac{1}{2x^2y^{10}}$$  

• $$-\frac{1}{2x^2y^{10}}$$  

• $$\frac{1}{128x^2y^{10}}$$  

• $$-\frac{1}{128x^2y^{10}}$$  

Multiple Choice

Simplify each sum or difference.

• $$-\sqrt{3}$$

• $$-\sqrt{9}$$

• $$-3$$

• $$-9\sqrt{2}$$

Multiple Choice

Simplify the expression completely.

$$\left(-\frac{2x^3y^{-2}}{2xy^0\cdot2y^{-1}}\right)^{^{-3}}$$  

• $$-\frac{8y^3}{x^6}$$  

• $$\frac{y^3}{8x^6}$$  

• $$\frac{8y^3}{x^6}$$  

• $$-8x^{-6}y^{-3}$$  

Multiple Choice

Simplify $$\sqrt{7}\left(\sqrt{175}+\sqrt{35}\right)$$  

• $$35+49\sqrt{5}$$  

• $$1225+7\sqrt{5}$$  

• $$35+7\sqrt{5}$$  

• $$70$$  

Multiple Choice

Simplify the expression completely.

$$\left(\frac{-2a^{-3}b^{-2}\cdot2b^3}{-2a^4b^2}\right)^{^{-4}}$$  

• $$-\frac{a^{28}b^4}{16}$$  

• $$\frac{a^{28}b^4}{16}$$  

• $$-16a^{28}b^4$$  

• $$16a^{28}b^4$$  

Multiple Choice

Simplify completely.

• -1
• -√5
• -6√5
• -30

Multiple Choice

Simplify $$\left(\sqrt{10}+3\right)\left(\sqrt{10}-3\right)$$  

• $$1$$  

• $$7$$  

• $$19$$  

• $$10-2\sqrt{3}$$  

Multiple Choice

Simplify each sum or difference.

• $$7\sqrt{80}$$

• $$\sqrt{22}$$

• $$44$$

• $$22\sqrt{2}$$

Multiple Choice

Simplify $$\frac{\sqrt{c^5}}{\sqrt{d^9}}$$  

• $$\frac{c^2\sqrt{cd}}{d^5}$$  

• $$\frac{c^2}{d^4}$$  

• $$\frac{c^2\sqrt{c}}{d^{4\sqrt{d}}}$$  

• $$\frac{c}{d}\sqrt{\frac{c}{d}}$$  

Multiple Choice

Simplify completely.

• -60
• -2√15
• -∛60
• -3∛20

Multiple Choice

Simplify $$5\sqrt{32}+\sqrt{27}+2\sqrt{75}$$  

• $$20\sqrt{2}+13\sqrt{3}$$  

• $$7\sqrt{100}$$  

• $$8\sqrt{100}$$  

• $$33\sqrt{5}$$  

Multiple Choice

Simplify each product.

• $$5\sqrt{3}-3\sqrt{5}$$

• $$\sqrt{75}-3$$

• $$5\sqrt{3}-5\sqrt{5}$$

• $$22\sqrt{2}$$

Multiple Choice

Simplify $$\left(4+2\sqrt{5}\right)\left(3\sqrt{3}+4\sqrt{5}\right)$$  

• $$12\sqrt{3}+16\sqrt{5}+40+6\sqrt{15}$$  

• $$12\sqrt{3}$$  

• $$16\sqrt{5}$$  

• $$40$$  

Multiple Choice

Simplify completely.

• √15
• 15
• 8
• 2√2

Multiple Choice

Simplify $$\frac{8}{\sqrt{6}-5}$$  

• $$\frac{\left(-40-8\sqrt{6}\right)}{19}$$  

• $$\frac{27-10\sqrt{3}}{13}$$  

• $$40$$  

• $$-2-\sqrt{2}$$  

Multiple Choice

Simplify each product.

• $$-8\sqrt{3}+12$$

• $$-8\sqrt{3}-12$$

• $$5\sqrt{3}-5\sqrt{5}$$

• $$-24-3\sqrt{3}$$

Multiple Choice

Simplify:

• $$\sqrt{5}$$

• $$\frac{\sqrt{14}}{2}$$

• $$\sqrt{7}$$

• Cannot be simplified

Multiple Choice

Simplify completely.

• √12
• 2√2
• 8
• 2√3

Multiple Choice

Simplify:

• A
• B
• C
• D

Multiple Choice

Simplify each product.

• $$10\sqrt{6}+6\sqrt{77}$$

• $$106+\sqrt{77}$$

• $$106+6\sqrt{77}$$

• $$\sqrt{106}+6\sqrt{7}$$

Multiple Choice

Simplify completely.

• ∛27
• 3∛3
• 3
• ∛12

Multiple Choice

Simplify each product.

• $$-\sqrt{6}$$

• $$-\sqrt{7}$$

• $$-\sqrt{8}$$

• $$-\sqrt{10}$$

Multiple Choice

Simplify completely.

• 3√15
• 12√3 - 9√15
• 3 - 4√3 - √15
• -36√15

Multiple Choice

Simplify each quotient.

• $$5\sqrt{2}+5$$

• $$5\sqrt{2}+8$$

• $$5\sqrt{2}+3$$

• $$5\sqrt{2}-3$$

Multiple Choice

Simplify completely.

• -60 - √90
• -12√90 + 20√15
• -36√10 + 20√15
• -12√21 + 20√15

Multiple Choice

Simplify each quotient.

• $$\frac{2\sqrt{6}-2\sqrt{11}}{5}$$

• $$\frac{2\sqrt{6}+2\sqrt{11}}{5}$$

• $$\frac{2\sqrt{6}-2\sqrt{11}}{2}$$

Multiple Choice

Simplify completely.

• 12√10 + 20√3
• 4√90 + 4√75
• 4√21 + 4√20
• 4√21 + 8√5

Multiple Choice

Simplify completely.

• -√20 + 4√12
• -√12 + 4√8
• 4√18
• -2√5 + 8√3

Multiple Choice

Simplify completely.

• -28 + 3x
• -28 + 9x
• -28 + 9x²
• -28 + 3x - 3√3x

Multiple Choice

Simplify completely.

• -4 + 5√k
• -4 + 2√5k - 2√5 + 5√k
• -4 + 5k
• -4 + 25√k

Multiple Choice

Simplify completely.

• 13
• 7 + 2√6
• 13 + 8√6
• 8√6

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Simplify:

• 6x²
• 18x²

Multiple Choice

Simplify:

• 2x√14x
• 4x√14x
• 2x√14x³
• 4x√14x³

Multiple Choice

In the picture, the "3" is called...

• the index
• the radical sign
• the radicand
• none

Multiple Choice

• A
• B
• C
• D

Multiple Choice

SIMPLIFY:

• A
• B
• C
• D

Multiple Choice

Simplify:

• 4√30
• √4√30
• √2√30
• 2√30

Multiple Choice

Simplify:

• A
• B
• C
• D

Multiple Choice

Simplify the expression:

• 6x²y² ∛3
• 6xy² ∛6x²
• ∛1296x⁵y⁶
• cannot combine; unlike radicand

Multiple Choice

Simplify:

• √5
• (√14)/2
• √7
• Cannot be simplified

Multiple Choice

Simplify completely.
∛(2⋅2⋅2⋅2⋅3⋅x⋅x⋅x⋅x⋅x⋅x⋅y⋅y⋅y)

• 2x²y∛6
• 4x³y√(3y)
• ∛(24x⁶y³)
• 8x²y∛6

Multiple Choice

Simplify completely.
7√5 + 3√5

• 21√5
• 10√10
• 10√15
• 10√5

Multiple Choice

Give the radical form.

• ∛7⁴
• ∜7³
• ∛4⁷
• ∜3⁷

Multiple Choice

What term is used for the 5?

• base
• radicand
• index
• exponent