powerpoint presentation

1. Subtitle

2. Principal Root
The positive square root of a number is called the principal root.
12 = (1 x 1) = 1
22 = (2 x 2) = 4
32 = (3 . 3) = 9
42 = (4) (4) = 16
52 = (5) (5) = 25
(-1)2 = 1
(-2)2 = 4
(-3)2 = 9
(-4)2 = 16
(-5)2 = 25

3. Irrational numbers (H)
▪ The set of irrational numbers is the set of numbers
which cannot be expressed as a ratio of two integers.
These numbers are equivalent to non-terminating and
non-repeating decimals.
Examples: 2 ; π = 3.1416… ; 5 ; 8 ; 17

4. To determine the integers before and after the square root of
a number, think of a perfect square number before and after the
given number. Then, solve for the roots.
Example 1: 11
9 = 3 (since 3 . 3 is 9) and
16 = 4 (since 4 . 4 is 16)
Therefore, 11 is between 3
and 4.
Example 2: 156
144 = 12 and 169 = 13
Therefore, 156 is between
12 and 13.

5. Example 3: 74
64 = 8 and 81 = 9
Therefore, 74 is between 8
and 9.
Example 4: 35
25 = 5 and 36 = 6
Therefore, 35 is between 5
and 6.

6. To estimate the square root of a number to the nearest
tenths and hundredths:
▪ 1. Think of two closest perfect square numbers before and after the
given number.
▪ 2. Solve for the roots and the use the first as the whole number.
▪ 3. Solve for the tenths digit by dividing the difference of the first perfect
square number from the given number by the difference of the first
perfect square number from the second perfect square number.
▪ 4 To estimate the square root of a number to the nearest hundredths,
identify a number whose square is closest to the given number.

7. Example 1. What is 𝟕 ?
4 = 2 and 9 = 3
so, it is between 2 and 3.
Let 7 = 2. x
7 −4
9 −4
=
3
5
= 0.6
Therefore the estimated square root of 7 to the
nearest tenths is 2. 6

8. To find the estimated hundredths, 2.64 < 7 < 2. 65
(2.64)2 = 6.9696 and (2.65)2 = 7.0225
Therefore the estimated square root of 7 to the nearest
hundredths is 2.65