1.4² = ??

≈ 2

1.7² = ??

≈ 3

2.25² = ??

≈ 5

≈ 2

14² = ??

196

 15² = ??

225

16² = ??

256

25² = ??

625

√2 = ?

≈ 1.4

√3 = ? ?

≈ 1.7

 √5 = ??

≈ 2.25

√625 = ??

25

√256 = ??

16

√225 = ?

15

How would you solve this:

Estimate √52

Find the closest perfect square roots either side of it that you DO know. So, √49 = 7 and √64 = 8

The estimate is around 7.1 or 7.2 ... √52 is closer to √49 than √64, therefore it's closer to 7 than 8

How would you estimate this:

4√5

You could multiply 4 by the approximate square root of 5 which is between 2 and 3 (closer to 2 though). However this results in a large margin of error, yielding an estimate of between 8 and 12...

Instead, you can often get a more accurate estimate by Combining the root and the coefficient, e.g.

√16 x √5 = √80 which is slightly less than

√81 therefore is slightly less than 9

Simplify

√72

√72 = √2 x √2 x √2 x √3 x √3 = 2 x 3 x √2 = 6√2 

(1/8)^-4/3 = ?

(1/8)^-4/3 = 8^4/3 = 3√8⁴ =  (3√8)⁴  = (2)⁴ = 16

 sq.rt (144 ÷ 16) = ? 

sqrt 72  ÷ sq rt 8 = ?

1. sqrt 144  ÷ sqrt 16 = 12 ÷ 4 = 3

2. sqrt (72 ÷ 8) =  sqrt 9 = 3