# SQUARE ROOTS OF  PERFECT SQUARES WORKSHEET

In the page "Square roots of perfect squares worksheet",  we are going to learn how to find square root of a number.

## What is square root?

Finding square roots of perfect squares :

Finding square roots is the opposite process squaring.

1²  =  1, the square root of 1 is 1.

2²  =  4, the square root of 4 is 2.

3²  =  9, the square root of 9 is 3.

4²  =  16, the square root of 16 is 4.

## Square roots of perfect squares worksheet - Practice questions

(1) Find square root of 324 by prime factorization

(2) Find square root of 625 by prime factorization

(3) Find square root of 4096 by prime factorization

(4) Find square root of 400 by prime factorization

(5) Find square root of 144 by prime factorization

(6) Find square root of 1024 by prime factorization

(7) Find square root of 256 by prime factorization

(8) Find square root of 2025 by prime factorization

(9) Find square root of 36 by prime factorization

(10) Find square root of 3136 by prime factorization

## Square roots of perfect squares worksheet - Solution

Question 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. Hence, square root of 324 is 18.

Let us see the solution of the next question on "Square roots of perfect squares worksheet".

Question 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

Hence, square root of 625 is 25.

Let us see the solution of the next question on "Square roots of perfect squares worksheet".

Question 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

Hence, square root of 4096 is 64.

Question 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

Hence, square root of 400 is 20.

Question 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

Hence, square root of 144 is 12.

Question 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

Hence, square root of 1024 is 32.

Question 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

Hence, square root of 256 is 16.

Question 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

Hence, square root of 2025 is 45.

Question 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

Hence, square root of 36 is 6.

Question 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

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

After having gone through the stuff given above, we hope that the students would have understood "Square roots of perfect squares worksheet".

Apart from the stuff given above, if you want to know more about "Square roots of perfect squares worksheet", please click here.

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments... WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6