# FINDING SQUARE ROOT BY PRIME FACTORIZATION METHOD

Thew following steps will be useful to find square root of a number by prime factorization.

(i)  Decompose the number inside the square root into prime factors.

(ii)  Inside the square root, for every two same numbers multiplied, one number can be taken out of the square root.

(iii) Combine the like square root terms using mathematical operations.

Example :

√27 + √9 - √12  =  √(3 ⋅ 3 ⋅ 3) + (3 ⋅ 3) - √(2 ⋅ 2 ⋅ 3)

√27 + √9 - √12  =  3√3 + √3 - 2√3

√27 + √9 - √12  =  2√3

## Practice Questions

Question 1 :

Find square root of 36 by prime factorization.

Decompose 36 into prime factors using synthetic division. √36  =  √(2 ⋅ 2 ⋅ 3 ⋅ 3)

√36  =  (2 ⋅ 3)

√36  =  6

Question 2 :

Find square root of 144 by prime factorization.

Decompose 144 into prime factors using synthetic division. √144  =  √(2 ⋅ ⋅ ⋅ ⋅ 3 ⋅ 3)

√144  =  (2 ⋅ ⋅ 3)

√144  =  12

Question 3 :

Find square root of 256 by prime factorization.

Decompose 256 into prime factors using synthetic division. √256  =  √(2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2)

√256  =  (2 ⋅ ⋅ ⋅ 2)

√256  =  16

Question 4 :

Find square root of 324 by prime factorization.

Decompose 324 into prime factors using synthetic division. √324  =  √(2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

√324  =  2 ⋅ 3 ⋅ 3

√324  =  18

Question 5 :

Find square root of 400 by prime factorization.

Decompose 400 into prime factors using synthetic division. √400  =  √(2 ⋅ ⋅ ⋅ ⋅ 5 ⋅ 5)

√400  =  (2 ⋅ ⋅ 5)

√400  =  20

Question 6 :

Find square root of 625 by prime factorization.

Decompose 625 into prime factors using synthetic division. √625  =  √(5 ⋅ 5 ⋅ 5 ⋅ 5)

√625  =  5 ⋅ 5

√625  =  25

Question 7 :

Find square root of 1024 by prime factorization.

Decompose 1024 into prime factors using synthetic division. √1024  =  √(2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2)

√1024  =  (2 ⋅ ⋅ ⋅ ⋅ 2)

√1024  =  32

Question 8 :

Find square root of 2025 by prime factorization.

Decompose 2025 into prime factors using synthetic division. √2025  =  √(5 ⋅ 5 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

√2025  =  (5 ⋅ 3 ⋅ 3)

√2025  =  45

Question 9 :

Find square root of 3136 by prime factorization.

Decompose 3136 into prime factors using synthetic division. √3136  =  √(2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 7 ⋅ 7)

√3136  =  (2 ⋅ ⋅ ⋅ 7)

√3136  =  56

Question 10 :

Find square root of 4096 by prime factorization.

Decompose 4096 into prime factors using synthetic division. √4096  =  √(2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2)

√4096  =  (2 ⋅ ⋅ ⋅ ⋅ ⋅ 2)

√4096  =  64 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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