This document provides instructions for estimating square roots without using a calculator. It explains that to estimate square roots: 1) You must know your perfect squares, which are numbers that are the product of a number multiplied by itself. 2) For numbers that are not perfect squares, the square root is estimated by finding the two adjacent perfect squares between which it falls and interpolating between them to the nearest tenth. 3) Examples are provided to demonstrate how to estimate the square roots of 27 and 64 by finding the nearest perfect squares and interpolating between them on a number line.

1. ESTIMATING SQUARE ROOT

2.  In order to estimate square
roots you must first know your
perfect square.
 A perfect square is the
number you get when you
multiply a number by itself.

3. For instance,
1 is a perfect square because 1x1 = 1
4 is a perfect square because 2x2 = 4
9 is a perfect square because 3x3 = 9
16 is a perfect square because 4x4 = 16

4. Recall some common perfect
square numbers.
𝟏 𝟐 = 1 𝟔 𝟐 = 36 𝟏𝟏 𝟐 = 121 𝟏𝟔 𝟐 = 256
𝟐 𝟐 = 4 𝟕 𝟐 = 49 𝟏𝟐 𝟐 = 144 𝟏𝟕 𝟐 =
289
𝟑 𝟐 = 9 𝟖 𝟐 = 64 𝟏𝟑 𝟐 = 169 𝟏𝟖 𝟐 =
324
𝟒 𝟐
= 16 𝟗 𝟐
= 81 𝟏𝟒 𝟐
= 196 𝟏𝟗 𝟐
= 361

5. 𝟖𝟏 = ?

6. 𝟖𝟏 = 9

7. 𝟑𝟔 = ?

8. 𝟑𝟔 = 6

9. 𝟐𝟕 = ?

10. 𝟐𝟕 = ?
Since 27 is not a perfect square,
have to use a method to calculate
it’s square root.

11.  Not all numbers are perfect squares.
 Not every numbers has an integer for
a square root.
 We have to estimate square roots for
numbers between perfect squares.

12. To calculate the square root of a
non-perfect square
1. Place the values of the adjacent
perfect squares on a number line.
2. Interpolate between the points to
estimate to the nearest tenth.

13. Example 1 : Estimate 𝟐𝟕
What are the perfect square on each
side of 27?
25 30 31 35 36
 One perfect square
that is less and one that
is greater.
 Mark the perfect squares 25 and 36
5x5 6x6

14. Estimate 𝟐𝟕 to the nearest tenth
half
5 6
25 30 31 35 36
27
Estimate 𝟐𝟕 = 5.2
 If we look at 27 on the
number line we see that is
closer to the perfect square
25. we figure out that the
middle is between 30 and
31(30.5).
 This tells us
that the
square root of
27 is closer to
5 than 6.

15.  Estimate : 𝟐𝟕 = 5.2
 Check : (5.2) (5.2) = 27.04

16. Example 2 :
Find the perfect square smaller and
larger than the given number.
𝟔𝟓 = ?

17. Take the square root.
smaller 𝟔𝟓 larger
𝟔𝟒 𝟖𝟏
is
between 8 and 9

18. Example 3 :
Between what two consecutive integers
the square root of the number can be
found?
𝟑𝟎
𝟐𝟓 𝟑𝟔
between 5 and 6