Approximating Square Roots: Techniques and Examples

The video tutorial provides a method to estimate the square roots of non-perfect squares by identifying the perfect squares between which the number lies. It uses examples of estimating the square roots of 32, 55, and 123, demonstrating how to determine the two integers between which the square root will fall. The tutorial emphasizes understanding the relationship between numbers and their squares, and how to use this to make rough estimates of square roots without a calculator.

What is the greatest perfect square less than 32?

• 25

• 36

• 49

• 16

What integer is immediately higher than the square root of 32?

• 7

• 8

• 5

• 6

Between which two integers does the square root of 55 lie?

• 6 and 7

• 7 and 8

• 8 and 9

• 5 and 6

What is the perfect square immediately less than 55?

• 36

• 49

• 81

• 64

What is the next perfect square greater than 55?

• 72

• 64

• 100

• 81

Approximately, what could be the value of the square root of 55?

• 8.0

• 7.1

• 7.8

• 7.5

What is the greatest perfect square less than 123?

• 169

• 121

• 100

• 144

Between which two integers does the square root of 123 lie?

• 12 and 13

• 11 and 12

• 13 and 14

• 10 and 11

What could be a close estimate for the square root of 123?

• 12.5

• 12.0

• 11.5

• 11.1

Which integer is immediately higher than the square root of 123?

• 11

• 12

• 14

• 13