Quiz about Algebra 2A Unit 6 Test Review – Radical Properties

Question 1

Simplify the expression. $$x^{12}·x^2·x^{-4}$$ = _______

Accepted Answer

$$x^{10}$$

Answer

$$x^4$$

Answer

$$x^{-96}$$

Answer

x

Question 2

Simplify the expression. $$\frac{4x^4}{8x^{-1}}$$ = _______

Accepted Answer

$$(1/2)x^5$$

Answer

$$2x^3$$

Answer

$$(1/2)x^3$$

Answer

$$4x^5$$

Question 3

Simplify $$-5x^9(3x^4)^3$$ = _______

Accepted Answer

$$-135x^{21}$$

Answer

$$-135x^{20}$$

Answer

$$-15x^{21}$$

Answer

$$-5x^{22}$$

Question 4

Simplify the expression. $$\left(\frac{(x^{-5})}{(3y^7)}\right)^{-2}$$ = _______

Accepted Answer

$$9x^{10}y^{14}$$

Answer

$$\frac{x^{10}y^{14}}{3}$$

Answer

$$\frac{9x^{10}y^{14}}{3}$$

Answer

$$9x^7y^{11}$$

Question 5

Simplify the expression. $$(2+\sqrt{7})^2$$ = _______

Accepted Answer

$$11+4\sqrt{7}$$

Answer

$$9+2\sqrt{7}$$

Answer

$$4+2\sqrt{7}$$

Answer

$$7+4\sqrt{7}$$

Question 6

Simplify. $$(4x−3)^2$$ = _______

Accepted Answer

$$16x^2−24x+9$$

Answer

$$16x^2 + 24x + 9$$

Answer

$$8x^2−6x+9$$

Answer

$$16x^2−12x+9$$

Question 7

Rationalize each fraction. $$\frac{5}{\sqrt{75}}$$ Fill in the blank with the rationalized form of the fraction.

Accepted Answer

$$\frac{\sqrt[]{3}}{3}$$

Answer

$$\frac{3\sqrt{3}}{5}$$

Answer

$$\frac{3\sqrt{5}}{1}$$

Answer

$$\frac{\sqrt{75}}{5}$$

Question 8

Simplify each imaginary number into standard form, a + bi. $$2i(7-4i)$$

Accepted Answer

8 + 14i

Answer

14 + 8i

Answer

-8 + 14i

Answer

8 - 14i

Question 9

Simplify each imaginary number into standard form, a + bi.

$$\frac{(3-5i)}{(-4+2i)}$$

Accepted Answer

$$-\frac{11}{10} + \frac{7}{10}i$$

Answer

$$\frac{7}{10} - \frac{11}{10}i$$

Answer

$$\frac{11}{10} + \frac{7}{10}i$$

Answer

$$-\frac{7}{10} - \frac{11}{10}i$$

Question 10

Simplify each imaginary number into standard form, a + bi.

$$\frac{3}{4-2i}$$

Accepted Answer

$$\frac{3}{5} + \frac{3}{10}i$$

Answer

$$\frac{3}{4} - \frac{3}{8}i$$

Answer

$$\frac{3}{8} + \frac{3}{4}i$$

Answer

$$\frac{3}{10} - \frac{3}{5}i$$

Question 11

Solve each equation.
$$-2x^2 = 20$$

Accepted Answer

$$\pm i\ \sqrt[]{10}$$

Answer

$$\pm\sqrt[]{-10}$$

Answer

$$\pm2i\sqrt[]{5}$$

Question 12

(r4)6

Accepted Answer

r24

Answer

10r

Answer

r10

Answer

24r

Question 13

(5³x²y⁴)⁰

Accepted Answer

1

Answer

5xy

Answer

0

Answer

5

Question 14

According to exponent rules, when we multiply the same base, we _______ the exponents.

Accepted Answer

Add

Answer

Multiply

Answer

Divide

Answer

Subtract

Question 15

According to exponent rules, when we divide same bases, we _______ the exponents.

Accepted Answer

subtract

Answer

add

Answer

multiply

Answer

divide

Question 16

When raising a power to a power, you __________________ the exponents.

Accepted Answer

Multiply

Answer

Add

Answer

Subtract

Answer

Divide

Question 17

Simplify

(2a²b⁴z)(6a³b²z⁵)

Accepted Answer

12a⁵b⁶z⁶

Answer

8a⁵b⁶z⁶

Answer

12a⁶b⁸z⁵

Answer

8a⁶b⁸z⁵

Question 18

Simplify

Accepted Answer

x4/3

Answer

3x10

Answer

36x10

Answer

3x4

Question 19

Question 19.

Accepted Answer

True

Answer

False

Question 20

$$\sqrt{243}$$

Accepted Answer

$$9\sqrt{3}$$

Answer

$$3\sqrt{3}$$

Answer

$$81\sqrt{3}$$

Answer

$$3\sqrt{81}$$

Question 21

$$\sqrt{216}$$

Accepted Answer

$$6\sqrt{6}$$

Answer

$$6\sqrt{4}$$

Answer

$$4\sqrt{6}$$

Answer

$$36\sqrt{6}$$

Question 22

$$\sqrt{300}$$

Accepted Answer

$$10\sqrt{3}$$

Answer

$$3\sqrt{10}$$

Answer

$$2\sqrt{150}$$

Answer

$$100\sqrt{3}$$

Question 23

$$\sqrt{-256}$$

Accepted Answer

16i

Answer

$$\sqrt[]{16i}$$

Answer

$$9i\sqrt{14}$$

Answer

$$18\sqrt{6}$$

Question 24

$$\sqrt{-294}$$

Accepted Answer

$$7i\sqrt{6}$$

Answer

$$6i\sqrt{2}$$

Answer

49i

Answer

$$49i\sqrt{6}$$

Question 25

$$\sqrt{-147}$$

Accepted Answer

$$7i\sqrt{3}$$

Answer

$$3i\sqrt{49}$$

Answer

$$6i\sqrt{3}$$

Answer

$$9i\sqrt{7}$$

Question 26

Simplify.

$$\frac{1}{\sqrt[]{3}}$$

Accepted Answer

$$\frac{\sqrt[]{3}}{3}$$

Answer

$$\frac{2\sqrt[]{3}}{3}$$

Answer

$$\frac{\sqrt[]{2}}{5}$$

Answer

$$\frac{\sqrt[]{6}}{3}$$

Question 27

Simplify.

$$\frac{\sqrt[]{4}}{\sqrt[]{3}}$$

Accepted Answer

$$\frac{2\sqrt[]{3}}{3}$$

Answer

$$\frac{2}{\sqrt[]{3}}$$

Answer

$$\frac{\sqrt[]{10}}{2}$$

Answer

$$\frac{2\sqrt[]{5}}{5}$$

Question 28

Simplify.

$$\frac{\sqrt[]{10}}{\sqrt[]{6}}$$

Accepted Answer

$$\frac{\sqrt[]{15}}{3}$$

Answer

$$\frac{2\sqrt[]{5}}{5}$$

Answer

$$\frac{\sqrt[]{5}}{5}$$

Answer

$$\frac{2\sqrt[]{3}}{3}$$

Question 29

Simplify.

$$\frac{\sqrt[]{10}}{\sqrt[]{15}}$$

Accepted Answer

$$\frac{\sqrt[]{6}}{3}$$

Answer

$$\frac{\sqrt[]{10}}{\sqrt[]{5}}$$

Answer

$$\frac{\sqrt[]{15}}{3}$$

Answer

$$\frac{\sqrt[]{15}}{5}$$

Question 30

Simplify.

$$\frac{\sqrt[]{12}}{\sqrt[]{15}}$$

Accepted Answer

$$\frac{2\sqrt[]{5}}{5}$$

Answer

$$\frac{\sqrt[]{5}}{2}$$

Answer

$$\frac{\sqrt[]{15}}{5}$$

Answer

$$\frac{2}{\sqrt[]{5}}$$

Question 31

Simplify.

$$\frac{-4}{\sqrt[]{3}}$$

Accepted Answer

$$-\frac{4\sqrt[]{3}}{3}$$

Answer

$$\frac{-4}{\sqrt[]{3}}$$

Answer

$$-\frac{\sqrt[]{3}}{4}$$

Answer

$$\frac{\sqrt[]{10}}{5}$$

Question 32

Simplify.

$$\frac{\sqrt[]{3}}{\sqrt[]{2}}$$

Accepted Answer

$$\frac{\sqrt[]{6}}{2}$$

Answer

$$\frac{\sqrt[]{6}}{3}$$

Answer

$$\frac{\sqrt[]{15}}{3}$$

Answer

$$\frac{\sqrt[]{10}}{2}$$

Question 33

Simplify.

$$\frac{\sqrt[]{8}}{\sqrt[]{12}}$$

Accepted Answer

$$\frac{\sqrt[]{6}}{3}$$

Answer

$$-2\sqrt[]{2}$$

Answer

$$\frac{\sqrt[]{6}}{2}$$

Answer

$$\frac{\sqrt[]{10}}{2}$$

Question 34

Simplify.

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 35

What is the conjugate of:
$$5+\sqrt{7}$$

Accepted Answer

$$5-\sqrt{7}$$

Answer

18

Answer

$$5+\sqrt{7}$$

Answer

32

Question 36

$$\frac{-2}{1+\sqrt{6}}$$ Rationalize the following:

Accepted Answer

$$\frac{-2+2\sqrt{6}}{-5}$$

Answer

$$\frac{1+\sqrt{6}}{-2}$$

Answer

$$-\frac{2\sqrt{6}}{6}$$

Answer

$$-2\sqrt{6}$$

Question 37

What is the conjugate of:
$$6-3\sqrt{2}$$

Accepted Answer

$$6+3\sqrt{2}$$

Answer

$$3\sqrt{2}+6$$

Answer

$$6-3\sqrt{2}$$

Answer

18

Question 38

Find the product:
(5n-8)(5n+8)

Accepted Answer

25n2-64

Answer

10n2

Answer

5n2+16

Answer

16

Question 39

Find the product:
(2x+3)²

Accepted Answer

4x2+12x+9

Answer

2x+3+2x+3

Answer

4x2+9

Answer

16x2+9

Question 40

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

Accepted Answer

3y³+ 7y²- 4y + 3

Answer

4y² + 3y³ - y + 3

Answer

-y⁴ + 2y³-y - 4

Answer

4y³+ 3y²-3y + 1

Question 41

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

Accepted Answer

-x²-6x + 8

Answer

x_² + 6x + 8

Answer

2x²+ 5x - 7

Answer

-2x² + 11x - 4

Question 42

Simplify the expression.
-3x²( 7x²- x + 4)

Accepted Answer

-21x⁴ + 3x³ -12x²

Answer

7x² - x + 4 (-3x²)

Answer

21x⁴+ 3x³+ 12x²

Answer

-12x²+ 3x³-21x⁴

Question 43

Multiply.
(b+3)(b²+2b+1)

Accepted Answer

b³+5b²+7b+3

Answer

b³+6b²+6b+3

Answer

4b³+8b²+3b

Answer

3b³+6b²+3b

Question 44

(5x⁴- 4x³- 2x² + x - 19) - (x⁴+ 5x³ + 8x² + x + 5)

Accepted Answer

4x⁴- 9x³- 10x²- 24

Answer

4x⁴- 9x³ - 10x²- 2x - 24

Answer

4x⁴ - 9x³ - 10x² + 2x - 24

Answer

-4x⁴ - 9x³ - 10x² - 24

Question 45

(2x + 3)(x² + 4x + 1)

Accepted Answer

2x³ + 11x² + 14x + 3

Answer

2x³ + 10x² + 14x + 4

Answer

-2x³ - 11x² + 14x + 5

Answer

x³ - 11x² + 14x + 3

Question 46

Simplify the expression
(x - 3)²

Accepted Answer

x² - 6x + 9

Answer

x2 + 9

Answer

x² + 6x - 9

Answer

x² + 6x + 9

Question 47

Subtract the following polynomials
$$\left(6x^2-3x+2\right)-\left(-4x^2+3x-6\right)$$

Accepted Answer

$$10x^2-6x+8$$

Answer

$$2x^2-4$$

Answer

$$10x^2+8$$

Answer

$$2x^2-6x-4$$

Question 48

Multiply the following polynomials $$\left(3x-2\right)\left(x^2+x-1\right)$$

Accepted Answer

$$3x^3+x^2-5x+2$$

Answer

$$3x^3+5x^2+5x-2$$

Answer

$$3x^3+x^2-5x-2$$

Answer

$$3x^3+5x^2+5x+2$$

Question 49

Multiply the following polynomials
$$\left(3x^2+3\right)\left(x+4\right)^2$$

Accepted Answer

$$3x^4+24x^3+51x^2+24x+48$$

Answer

$$3x^4+48x^3+3x^2+48$$

Answer

$$3x^4+15x^2+12$$

Answer

$$3x^4-45x^2-48$$

Question 50

Add the following polynomials $$\left(3x-2x^2+3x^3-2\right)+\left(3x^2-2x-9\right)$$

Accepted Answer

$$3x^3+x^2+x-11$$

Answer

$$3x^3+x^2+5x+7$$

Answer

$$3x^3-x^2+x-11$$

Answer

$$3x^3+x^2-x-7$$

Question 51

Simplify the expression.
2x(-2x - 3)

Accepted Answer

-4x2 - 6x

Answer

-4x - 3

Answer

x2 - 3

Answer

-4x - 6

Question 52

Add the polynomials (x-2) and (x²+3)

Accepted Answer

x2+x+1

Answer

x3+5

Answer

x3+1

Answer

x3-1

Question 53

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

Accepted Answer

2x² + x - 10

Answer

2x² + x + 2

Answer

x + 2

Answer

x - 10

Question 54

Add or Subtract to Simplify:
(5x + 2) + (4x + 5)

Accepted Answer

9x+7

Answer

9x -7

Answer

-9x-11

Answer

x+7

Question 55

In the movie Clueless, how does Cher help the new girl, Tai?

Accepted Answer

she gives her a makeover

Answer

she gives her the homework

Answer

she shows her the school

Answer

she doesn't help her

Question 56

In the movie Matilda, what is Matilda's power?

Accepted Answer

Telekinesis

Answer

Photosynthesis

Answer

Mind Reading

Answer

Flying

Question 57

In the little mermaid, what did Ariel give up in order to get a pair of legs?

Accepted Answer

her voice

Answer

her hair

Answer

her sight

Answer

her best friend flounder

Question 58

Simplify the following expression:

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 59

Which movie is this from?

Accepted Answer

Back to the Future

Answer

Stand by Me

Answer

Space Balls

Answer

Return of the Jedi

Question 60

who is simbas  dad

Accepted Answer

mufasa

Answer

scar

Answer

nala

Answer

rafiki

Question 61

(7-5i)(7+5i)

Accepted Answer

74

Answer

75

Answer

74-1

Question 62

Calculate:
i + 6i

Accepted Answer

7i

Answer

6i2

Answer

5i

Answer

7i2

Question 63

.

Accepted Answer

10i

Answer

10

Answer

-10

Answer

-10i

Question 64

What letter usually represent imaginary number?

Accepted Answer

i

Answer

a

Answer

j

Answer

x

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