SQUARE ROOT PRACTICE PROBLEMS

why sqrt(36) is just positive 6
why sqrt(36) is just positive 6

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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