Question

Can someone explain me how to find square root by prime factorization ?

Answer 1

Answer:

STEPS

• 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.

Example

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