G8

Input/Model

(Teacher Presents)

Directions: Estimate the decimal value. Use a calculator to check.

−√ 75

Solution:

−√ 75 can be thought of as (- 1) • −√ 75

−√ 75 can be approximated in the same manner and multiplied by –1

When considering√ 75 on a number line, the perfect square less than 75 is 64

• (^) √ 64 = 8

The perfect square greater than 75 is 81.

• (^) √ 81 = 9
• Now make the statement (^) √ 64 < √ 75 < √ 81.

Simplify 8 <√ 75 < 9

Recall, −√ 75 = (–1) •√ 75. Therefore, −√ 75 is between –8 and –9.

Calculator: −√ 75 ≈−8.7

√

150 2

Solution:

First, focus on √ 150

On a number line, the perfect square less than 150 is 144.

• (^) √ 144 = 12

The perfect square greater than 150 is 169.

• (^) √ 169 = 13

Now, make the statement √ 144 < √ 150 <√ 169.

Simplify 12 <√ 150 < 13

So, √ 150 is between 12 and 13.

Looking at the original ratio, √^1502 I can now make the statement that, √^1502 is between^122 and^132 or 6 <

√ 150 < 6.5

Calculator: √^1502 ≈6.1

Input/Model