Intro to Simplifying Square Roots

Review:

The Square root of 16 is basically asking what number times itself is 16?

Since (4)(4) = 16, then √16 = 4

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here's another...√144 = 12, since (12)(12) = 144​

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By Amy Helfenbein

​It is important to be able to recognize the perfect Squares.

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....You can also use your calc, it is much faster to just recognize them.​

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Multiple Choice

What is √81

• 8

• 12

• 8.1

• 9

Multiple Choice

What is √ 36

• 4

• 6

• 9

• 12

Multiple Choice

what is √121

• 9

• 10

• 11

• 12

​WHAT DO WE DO IF IT IS NOT A PERFECT SQUARE?

..... Look for perfect square factors.

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Let's practice just finding perfect squares that are factors....

Multiple Choice

Which perfect square fits in √12

• 4

• 3

• 6

• 2

Multiple Choice

Which perfect square fits in √50

• 5

• 10

• 25

• 2

Multiple Select

Which perfect square fits in √72

... careful there are two that work

• 9

• 16

• 25

• 36

Multiple Choice

Which perfect square fits in √200

there are three that work

BUT PICK THE LARGEST ONE!

• 4

• 16

• 25

• 100

​Now let's work on breaking them down.

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Examples:

√200 = ​(√100)(√2) = 10√2

√12 = ​(√4)(√3) = 2√3

√72 = ​(√36)(√2) = 6√2​

√50 = ​(√25)(√2) = 5√2​

REMINDER!!!!

We need PERFECT SQUARE FACTORS...​

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😱This does not help, since they are not perfect squares:

√ 50 = ​(√10)(√5) = ???

√12 = ​(√6)(√2) = ???

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Multiple Choice

Which is the correct way to simplify √27

• √27 = (√9)(√3)

  = 3√3

• √27 = (√9)(√3)

  = 9√3

Multiple Choice

Which is the correct way to simplify √75

• √75 = (√5)(√15)

• √75 = (√25)(√3)

  = 5√3

Multiple Choice

Which is the correct way to simplify √120

• √120 = (√4)(√30)

  = 2√30

• √120 = (√12)(√3)

Multiple Choice

Simplify √108

• 3√12

• 4√27

• 8√2

• 6√3

Multiple Choice

Simplify:
 √40

• 4√10
• 10√4
• 2√10
• 10√2

Multiple Choice

Simplify:
√96

• 4√6
• 3√6
• 6√5
• 6√8

Multiple Choice

Simplify √20

• $$2\sqrt{5}$$

• 10

• $$5\sqrt{2}$$

• $$\sqrt{10}$$

Multiple Choice

Simplify $$\sqrt{45}$$  

• $$5\sqrt{9}$$  

• $$5\sqrt{3}$$  

• $$3\sqrt{5}$$  

• $$9\sqrt{5}$$  

Multiple Choice

Simplify $$\sqrt{125}$$  

• $$3\sqrt{5}$$  

• $$5\sqrt{5}$$  

• $$3\sqrt{25}$$  

• $$5\sqrt{3}$$  

See you tomorrow!​

ALL DONE