Simplifying square roots

Do these expressions have another exact representation of the value?

4

8

13

Yes, the square root of 4 is also 2 because 2 times 2 equals 4.

Yes, the square root of 8 is also 2 times the square root of 2 or 2 square roots of 2 which is also written as 2 .

No, the square root of 13 can not be renamed or simplified.

2

Standard: M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation. g. Simplify, add, subtract, multiply, and divide expressions containing square roots.

Essential Question:

How do I simplify a square root?

In the expression ,

is the radical sign and64 is the radicand.

If 92 = 81 then 9 is a square root of 81 or = 9.

64

81

1. Find the principle square root of 64. This is also written as .

64

64 = 8

2. Find the negative square root of 0.04. This is also written as : .

0.04

0.04

= - 0.2

[reminder: .04 is 4 hundredths; the square root of 4 is 2; the square root of one hundredth is one tenth]

11, -11 This can also be written ±11.

4. Find the square root:21

5. Find the square root:

3. Find the square roots: 121

441

25

81

5

9

1 x 1 = 12 x 2 = 43 x 3 = 9

4 x 4 = 165 x 5 = 256 x 6 = 36

49, 64, 81, 100, 121, 144, ...

What numbers are squares?

1. Simplify Factor 80. 80 = 2 x 2 x 2 x 2 x 5

80

20 2 2 2 58 x x x x

[2x2]x[2x2]x5

You did it! =

Now, you may “take out” pairs of like factors

[2x2]x[2x2]x5 4 5

80 4 5

=

2. SimplifyFactoring 180 into prime factors

you get

2 x 2 x 3 x 3 x 5.

180

= [2 x 2 x 2 x 2] x [3 3 x x 3 x 5 3] x 5

2 x 3 5 = 6 5

Yes! Good job!

180 = 6 5

Now, try one by yourself. Simplify and see if your answer is below.

1. .

2. .

3. .

4..

72

3 8

6 236 2

2 18 Did you get it? Congratulations!!!

3. Simplify

Simplify the numerator and denominator.

25

49

25 5 =

749

4. Simplify

Simplify the numerator and denominator.

100

25

100 10 = = 2

525

You could also solve this problem by dividing 100 by 25 first. Let’s see that. 100

= 4 = 225

Cool, huh? Both ways work so you have a choice.

Please work these problems showing all steps.

1. 2. 3. 4.

54 75 108 500

1.

3 6 6 3 10 55 32. 3. 4.

Anything we need to go back over before we continue?

5. 6. 7. 8.

Good job! Now, work these problems showing all steps.

50

8132

121

275

25

48

64

5.

5 2 5 = 2

9 96.

4 2 4 = 2

11 11

7. 11 8. 3 1

= 32 2

How do I simplify a square root?

Now, practice by completing your

worksheet.