Please do watch my first ever slide share presentation especially to those students who love math. I hope you will learn from this.

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

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 𝟐
= 25 𝟏𝟎 𝟐
= 100 𝟏𝟓 𝟐
= 225 𝟐𝟎𝟎 𝟐
= 400

5. 𝟖𝟏 = ?

6. 𝟖𝟏 = 9

7. 𝟑𝟔 = ?

8. 𝟑𝟔 = 6

9. 𝟐𝟕 = ?

10. 𝟐𝟕 = ?
Since 27 is not a perfect square, we
have to use a method to calculate
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