SQUARE ROOT PRACTICE PROBLEMS

Problem 1 : 

Find square root of 324 by prime factorization.

Solution :

Step 1 :

Split 324 into prime factors.

Step 2 :

√324  =  √2 x 2 x 3 x 3 x 3 x 3

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

So, square root of 324 is 18.

Problem 2 : 

Find square root of 625 by prime factorization.

Solution :

Step 1 :

Split 625 into prime factors.

Step 2 :

√625  =  √5 x 5 x 5 x 5

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

=  5 x 5

=  25

So, square root of 625 is 25.

Problem 3 : 

Find square root of 4096 by prime factorization.

Solution :

Step 1 :

Split 625 into prime factors.

Step 2 :

√4096  =  √2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 3 :

Take one common number from the radical

=  2 x 2 x 2 x 2

=  64

So, square root of 4096 is 64.

Problem 4 : 

Find square root of 400 by prime factorization.

Solution :

Step 1 :

Split 400 into prime factors.

Step 2 :

√400  =  √2 x 2 x 2 x 2 x 5 x 5

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

=  2 x 2 x 5

=  20

So, square root of 400 is 20.

Problem 5 : 

Find square root of 144 by prime factorization.

Solution :

Step 1 :

Split 144 into prime factors .

Step 2 :

√144  =  √2 x 2 x 2 x 2 x 3 x 3

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

=  2 x 2 x 3

=  12

So, square root of 144 is 12.

Problem 6 : 

Find square root of 1024 by prime factorization.

Solution :

Step 1 :

Split 1024 into prime factors.

Step 2 :

√1024  =  √2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

=  2 x 2 x 2 x 2 x 2

=  32

So, square root of 1024 is 32.

Problem 7 : 

Find square root of 256 by prime factorization.

Solution :

Step 1 :

Split 256 into prime factors.

Step 2 :

√256  =  √2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

=  2 x 2 x 2 x 2

=  16

So, square root of 256 is 16.

Problem 8 : 

Find square root of 2025 by prime factorization.

Solution :

Step 1 :

Split 2025 into prime factors .

Step 2 :

√2025  =  √5 x 5 x 3 x 3 x 3 x 3

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

=  5 x 3 x 3

=  45

So, square root of 2025 is 45.

Problem 9 : 

Find square root of 36 by prime factorization.

Solution :

Step 1 :

Split 36 into prime factors.

Step 2 :

√36  =  √2 x 2 x 3 x 3

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

=  2 x 3

=  6

So, square root of 36 is 6.

Problem 10 : 

Find square root of 3136 by prime factorization.

Solution :

Step 1 :

Split 3136 into prime factors.

Step 2 :

√3136  =  √2 x 2 x 2 x 2 x 2 x 2 x 7 x 7

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

=  2 x 2 x 2 x 7

=  56

So, square root of 3136 is 56. Square roots of perfect squares worksheet

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