wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

How to do square root while using pythogoras property

Open in App
Solution

Step I: Obtain the given number.
Step II: Resolve the given number into prime factors by successive division.
Step III:Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
Step IV: Take one factor from each pair.
Step V: Find the product of factors obtained in step IV.
Step VI: The product obtained in step V is the required square root.

Square root by prime factorization method

Example 1

Find the square root of 1156.
1156 = 2 x 578
= 2 x 2 x 289
= 2 x 2 x 17 x 17
∴ √1156 = √(2 x 2 x 17 x 17)
√1156 = 2 x 17
√1156 = = 34
__________________________________________________________________
Example 2

Find the square root of 324.
324 = 2 x 162
= 2 x 2 x 81
= 2 x 2 x 3 x 27
= 2 x 2 x 3 x 3 x 9
= 2 x 2 x 3 x 3 x 3 x 3
∴ √324 = √(2 x 2 x 3 x 3 x 3 x 3)
√324 = 2 x 3 x 3
√324 = 18

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Square Roots of Perfect Squares
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon