Surds Mult Div Add Subt Rationalizing

Intro

Simplifying

Multiple Choice

Simplify $$\sqrt{56}$$  

• $$2\sqrt{14}$$  

• $$4\sqrt{14}$$  

• $$2\sqrt{28}$$  

• $$2\sqrt{9}$$  

Add and Subtract

• Simplify First

• Combine like terms (terms with the same radicand)

• ONLY outside numbers are added (radicans DO NOT change once they are simplified)

Multiple Select

What kind of terms can be added or subtracted? (Check all that apply)

• Like terms

• Common terms

• Terms with the same radicand

Multiple Choice

Add

$$\sqrt{2}+3\sqrt{2}$$  

• $$2\sqrt{2}$$  

• $$3\sqrt{4}$$  

• $$4\sqrt{2}$$  

• $$4\sqrt{4}$$  

Multiple Choice

Add

$$\sqrt{27}+2\sqrt{12}$$  

• $$3\sqrt{3}+4\sqrt{6}$$  

• $$7\sqrt{3}$$  

• $$12\sqrt{3}$$  

• $$7\sqrt{6}$$  

Multiply

• Multiply the outside numbers

• Multiply the inside numbers

• Simplify

Operations

More egs

More egs

Rationalization of the Denominator of a Surd..

More egs

More complicated examples

More complicated examples

Multiple Choice

What is the largest perfect square that you use to simplify

$$\sqrt{24}$$  

• 1

• 4

• 9

• 16

Multiple Choice

Simplify

$$\sqrt{24}$$  

• $$4\sqrt{6}$$  

• $$2\sqrt{6}$$  

• $$6\sqrt{2}$$  

• $$6\sqrt{4}$$  

What if you have variables?

1. Make sure the variable is an even power
2. If it's not even, subtract one from the exponent and rewrite as a product
3. Take the variable with the even power and divide by 2 - put that on the outside of the radical

Multiple Choice

Simplify:

$$\sqrt{x^{15}}$$  

• $$x^{7.5}$$  

• $$x^{14}\sqrt{x}$$  

• $$x^7\sqrt{x}$$  

Multiple Choice

Simplify:

$$\sqrt{x^2y^7}$$  

• $$xy^3$$  

• $$xy^3\sqrt{y}$$  

• $$xy^3\sqrt{xy}$$  

Multiple Choice

Simplify:

$$\sqrt{80x^2y^4}$$  

• $$2xy^2\sqrt{20}$$  

• $$4xy^2\sqrt{5}$$  

Multiple Choice

Simplify:

$$2\sqrt{24}+5\sqrt{54}$$  

• $$7\sqrt{78}$$  

• $$19\sqrt{6}$$  

• $$7\sqrt{6}$$  

Multiple Choice

Multiply:

$$3\sqrt{8}\times4\sqrt{10}$$  

• $$12\sqrt{80}$$  

• $$7\sqrt{80}$$  

• $$24\sqrt{20}$$  

• $$48\sqrt{5}$$  

Multiple Choice

What is a surd?

• A recurring decimal

• An irrational number

• A fraction

• A rational number

Multiple Select

Which of the following are surds?

• $$\frac{\pi}{2}$$

• $$\sqrt{5}$$

• $$\left(\sqrt{17}\right)^2$$

• $$\sqrt{3}$$

• $$\sqrt{2}+1$$

Multiple Choice

Simplify:

• 1/5

• 20/100

• 2/10

• 1/√25

Fill in the Blank

Simplify $$\frac{\sqrt[]{42}}{\sqrt[]{6}}=\ \sqrt[]{}$$  

Multiple Choice

$$\sqrt{7}\times\sqrt{7}=$$  

• $$7$$  

• $$49$$  

• $$\sqrt{7}$$  

• $$14$$  

Multiple Choice

$$4\sqrt{5}=$$  

• $$\sqrt{80}$$  

• $$\sqrt{100}$$  

• $$\sqrt{20}$$  

• $$\sqrt{9}$$  

Multiple Choice

Which number is a rational number ?

• 1/4
• π
• √3
• ∛25

Multiple Choice

Which of these is an example of an irrational number?

• √2

• √1

• √9

• √25

Multiple Choice

Numbers like -3, -2, -1, 0, 1, 2, 3 are called

• whole numbers
• integers
• rational numbers
• natural numbers

Multiple Choice

Fully simplify....

Multiple Choice

Simplify: 
√(a²)

• a
• a²
• a^.5
• already simplified

Multiple Select

which numbers are rational numbers.

• 0.3333........

• π

• √5

• 5

Multiple Choice

Multiply and simplify; $$4\sqrt{6}\cdot\sqrt{3}$$  

• $$4\sqrt{9}$$  

• $$\sqrt{72}$$  

• $$4\sqrt{18}$$  

• $$12\sqrt{2}$$  

Multiple Choice

$$\sqrt{6}\left(2\sqrt{6}\right)$$  

• 12

• $$12\sqrt{6}$$  

• $$2\sqrt{36}$$  

• $$\sqrt{72}$$  

Multiple Choice

$$\sqrt{5}\left(3-\sqrt{6}\right)$$  

• $$\sqrt{15}-\sqrt{30}$$  

• $$3\sqrt{5}-\sqrt{30}$$  

• $$-\sqrt{15}$$  

• $$\sqrt{15}-\sqrt{18}$$  

Multiple Choice

$$\sqrt{2}\left(4\sqrt{10}-6\sqrt{6}\right)$$  

• $$8\sqrt{10}-6\sqrt{12}$$  

• $$4\sqrt{12}-6\sqrt{8}$$  

• $$4\sqrt{20}-6\sqrt{12}$$  

• $$8\sqrt{5}-12\sqrt{3}$$  

Multiple Choice

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

• $$20\sqrt{2}-14\sqrt{6}+2\sqrt{3}$$  

• $$46-14\sqrt{6}$$  

• $$32\sqrt{6}$$  

• $$40-14\sqrt{6}+6\sqrt{3}$$  

Multiple Choice

$$\left(10-3\sqrt{2}\right)\left(10+3\sqrt{2}\right)$$  

• $$82-\sqrt{2}$$  

• $$20-6\sqrt{2}$$  

• $$100-60\sqrt{2}$$  

• 82

Multiple Choice

Find the area of the rectangle

• 11

• $$22\ +3\sqrt{6}$$

• $$22+\sqrt{42}-2\sqrt{6}$$

• $$34+11\sqrt{6}$$

Multiple Choice

If √3x = 5√3 , what is x?

• 5
• 25
• 15
• 45

Multiple Choice

$$\sqrt{3}\div\sqrt{3}=$$  

• $$1$$  

• $$3$$  

• $$0$$  

• $$\sqrt{3}$$  

Multiple Choice

$$\sqrt{5}+\sqrt{5}=$$  

• $$2\sqrt{5}$$  

• $$0$$  

• $$5$$  

• $$\sqrt{10}$$  

Multiple Choice

$$2\sqrt{5}+3\sqrt{5}=$$  

• $$5\sqrt{5}$$  

• $$6\sqrt{5}$$  

• $$5\sqrt{10}$$  

• $$6\sqrt{10}$$  

Multiple Choice

Subtract the radical expressions below

$$4\sqrt[]{12}-5\sqrt[]{27}$$  

Hint: SImplify $$\sqrt[]{12}$$ and $$\sqrt[]{27}$$ first. Look back to slide 3, if needed.

• $$-7\sqrt[]{39}$$  

• $$-7\sqrt[3]{3}$$  

• $$-\sqrt[]{15}$$  

• $$-7\sqrt[]{3}$$  

Multiple Choice

Add the radical expressions below and simplify the result.

$$9\sqrt[]{2}+12\sqrt[]{3}$$  

• $$21\sqrt[]{5}$$  

• $$21\sqrt[]{2}$$  

• $$21\sqrt[]{3}$$  

• Already simplified.  One cannot add these since the two radicands are simplified and are not exactly the same.

Multiple Choice

Rationalise the Denominator:
³/_√5

• ^3√5/₅
• ^3√5/₂₅
• ^√5/₅
• ^√5/3

Multiple Choice

Fully simplify....

Multiple Choice

What should you multiply $$\frac{6}{1-\sqrt{5}}$$  by to rationalize the denominator?

• -4

• $$1-\sqrt{5}$$  

• $$1+\sqrt{5}$$  

• $$-\frac{\left(3-3\sqrt{5}\right)}{2}$$  

Multiple Choice

Rationalize the following: $$\frac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}$$  

• $$\frac{\sqrt{6}-\sqrt{10}}{8}$$  

• $$\frac{\sqrt{6}-\sqrt{10}}{-2}$$  

• $$\frac{\sqrt{6}+\sqrt{10}}{8}$$  

• $$\frac{2\sqrt{3}+2\sqrt{5}}{-2}$$  

Multiple Choice

Rationalize each denominator. Simplify the answer. $$\frac{4}{1\ +\sqrt{3}}$$  

• $$2\ -2\sqrt{3}$$  

• $$-2\ +2\sqrt{3}$$  

• $$4\ -2\sqrt{3}$$  

• $$-4\ -2\sqrt{3}$$  

Multiple Choice

Rationalize the denominator. Simplify the answer. $$\frac{5\ +\sqrt{3}}{2\ -\sqrt{3}}$$  

• $$13\ +7\sqrt{3}$$  

• $$-13\ +7\sqrt{3}$$  

• $$13\ -7\sqrt{3}$$  

• $$13\ +\sqrt{3}$$  

Multiple Choice

Multiply

$$2\sqrt{12}\times3\sqrt{7}$$  *Remember to simplify*

• $$6\sqrt{84}$$  

• $$5\sqrt{19}$$  

• $$12\sqrt{21}$$  

• $$8\sqrt{10}$$