1. Square Root of Decimal number

2. 66 = 2  3  11 Recap of Prime Factorization method
Example: Express 66 as a product of its prime factors
66 is an even number so can be written as 2  something...
List the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19... 66
33 can be written as
3 something... 2 33
11 is a prime number, so stop the process 3 11
Prime factorization is the product of multiplying it’s prime factors.
66 = 2  3  11
This is called a factor tree. All the red digits are prime factors of 66.

3. Recap of Converting Decimal to Fraction
Example: Convert 2.25 to Fraction
Solution:
Step 1: We have 2 decimal points in 2.25
Step 2: We have to multiply and divide it by 100
Example: Convert 0.5 to Fraction
Solution:
Step 1: We have 1 decimal point in 0.5
Step 2: We have to multiply and divide it by 10
Recap of Converting Fraction to Decimal
Added this slide
To divide a decimal number by 10 or 100, simply move the decimal point 1 or 2 steps to the left
e.g ÷ 10 = 5.0 ÷ 10
= 0.5
move the decimal point 1 step to the left
e.g ÷ 100 = ÷ 100
= 2.25
move the decimal point 2 steps to the left

4. Steps to follow to find Square Roots of Decimals using Prime Factorization method
Convert the decimals into fraction by multiplying and dividing by 100. Break the
fraction as numerator and denominator separately.
Prime factorize the numerator and denominator separately
Make pairs of factors from prime factorization
Find the square root of the number and write in the fraction form
Convert the fraction obtained to decimal numbers by simply moving the
decimal point 1-2 steps to the left.

5. Step 1: Convert the decimals into fraction by multiplying and dividing
Example 1: Find √12.25
Solution:
We know:
Step 1: Convert the decimals into fraction by multiplying and dividing
by 100 and break it as numerator and denominator
Step 2: Prime factorize 1225 and 100 separately
1225 = 5 x 5 x 7 x 7
100 = 2 x 2 x 5 x 5
Step 3: Make pairs of factors from previous step
122 = 5²
x 7²
100 = 2²
x 5²
Step 4: Find the square root of the number
and write in the fraction form
= 5
x 7
= 35
= 2
x 5
= 10
Step 5: Convert the fraction obtained to
decimal numbers by simply moving
the decimal point 1 step to the left.
Ans:

6. Step 1: Convert the decimals into fraction by multiplying and dividing
Example 2: Find √17.64
Solution:
We know:
Step 1: Convert the decimals into fraction by multiplying and dividing
by 100 and break it as numerator and denominator
Step 2: Prime factorize 1764 and 100 separately
1764 = 2 x 2 x 3 x 3 x 7 x 7
100 = 2 x 2 x 5 x 5
Step 3: Make pairs of factors from previous step
1764 = 2²
x 3²
x 7²
100 = 2²
x 5²
Step 4: Find the square root of the number
and write in the fraction form
= 2
x 3
x 7
= 42
= 2
x 5
= 10
Step 5: Convert the fraction obtained to
decimal numbers by simply moving
the decimal point 1 step to the left.
Ans:

7. Try These
Find √33.64
Find √96.04
Find √27.04