Square and Square Root – Quantitative Aptitude

Quantitative Aptitude – Square and Square Root

Square and Square root, these are the basics of any mathematical calculations. In quantitative aptitude you will need Square and Square root in many calculations. So you must do this chapter very carefully.

If you remember, you do this thing in your school days. It’s not so hard to learn. You just need to know the rules of How to find out Square and Square roots. In exam you may get questions directly from this chapter, but you will surely get a question which is related with Square and Square root.

Now we will discuss Square and Square root in details.

What is Square ?

A Square is a nothing but multiplication a number with the same number. Say, we need to find the Square of number 4. So we have to multiply the number 4 with 4.

4 x 4 = 16

We denote a Square as X². A small 2 is written at the upper right corner of that number. Few other Squares are :

2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25 …

What is Square Root ?

Finding Square root is the opposite of finding Square. Its the exact reverse process of finding Square. It is denoted as √9. Here X is any number.

For example, √16 is 4. because we know that Square of 4 is 16.

Students should memorize Squares upto 20. This would help you to do your Square root problems quickly. Sometimes you may get a question where the Square root be in fractional number. Those are also done in the similar way as you do in normal problems.

For example, What is the Square root of 20. The answer is 4.4721. The smaller but nearest exact Square root of 20 is 16. Square root of 16 is 4. Now the rest 4 will be calculated as same way and you will get an answer of 0.4727.

Few Examples to Test your Square And Square Root learnings:

Example #1

Find the value of:

A. 1/5

B. 11/5

C. 13/5

D. 16/5

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Correct Answer is: 16/5 [Option D].

How to Solve:

So, to find the value of the given expression, we need to simplify this.

Therefore,

or,

so,

or,

finally,

Therefore, the value of the given expression is 16/5.

Rough Workspace:

Example #2

is how much bigger than

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Correct Answer is:

[Option A].

How to Solve:
So, to find the answer, we need to find the difference between these two numbers.

Therefore,

or,

so,

finally,

Therefore, the

bigger than

Rough Workspace:

Example #3

Find the smallest perfect square number which is divisible by 3, 4, 5, 6 and 8.

A. 800

B. 1200

C. 2400

D. 3600

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Correct Answer is: 3600 [Option D].

How to Solve:
So, to find the smallest perfect square number which is divisible by 3, 4, 5, 6 and 8, we need to apply some mathematical rules.

Firstly, we need to find the LCM of all five numbers.
So, LCM of 3, 4, 5, 6 and 8 is: 120.

Also, we can say, 120 = 2 x 2 x 2 x 3 x 5.

Now, to make it a perfect square we need to multiply it by 2 x 3 x 5.
or, 2 x 2 x 2 x 3 x 5 x 2 x 3 x 5
or, 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5
finally, 3600.

Therefore, the smallest perfect square which is divisible by 3, 4, 5, 6 and 8 is 3600.

Rough Workspace:

Example #4

If,

, then find the value of n.

A. 5

B. 6

C. 7

D. 8

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Correct Answer is: 8 [Option D].

How to Solve:

So, to find the value of n in this statement, we need to simplify the statement.

Therefore,

or,

As 5⁴ is equal to 625

or,

Squaring both sides

so,

or,

finally,

Therefore, the value on n in the given statement will be 8.

Rough Workspace:

Example #5

and

, then find the value of:

A. 22

B. 26

C. 30

D. 34

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Correct Answer is: 34 [Option D].

How to Solve:
So, to find the value of

, firstly we need to simplify the value of X and Y.

As we know,

or,

multiplying both numerator and denominator with

or,

so,

or,

so,

or,

Similarly,

or,

multiplying both numerator and denominator with

And, by doing the same process as we do for X, we will get,

Now, putting the value of X and Y in the given equation we get,

or,

finally,

Therefore, the vale of the given equation is 34.

Rough Workspace:

Example #6

Find the value of:

A. 15

B. 18

C. 21

D. 23

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Correct Answer is: 18 [Option B].

How to Solve:

So, to find the value of the given expression, we need basic square root techniques.

Therefore, the value would be,

or,

so,

or,

finally,

So, the value of the given expression is, 18.

Rough Workspace:

Example #7

A group of people decided to plant trees such that, each member of the group will plant as many trees as the total number of members of that group. If they planted total 9216 trees, then find the total number of members in that group.

A. 93

B. 96

C. 97

D. 99

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Correct Answer is: 96 [Option B].

How to Solve:
So, the finding of the answer is very simple for this question. you need to just square root of the total numbers given in the question.

Now, as the question says that, each member of that group have to plant same number of trees as the total number of group members. And, we have total number of planted trees i.e, 9216.

So, if we square root the number 9216, we will get the total number of group member.

or,

Therefore, the total number of group members are 96.

Rough Workspace:

Example #8

What is the largest four digit perfect square?

A. 9801

B. 9900

C. 9908

D. 9999

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Correct Answer is: 9801 [Option A].

How to Solve:
So, here in this question we need to find the largest four digit perfect square.

Now, we know that 10000 is a perfect square. But, it is a five digit number.
The square root of 10000 is 100.

So, to make it a four digit number, the square value must be less that 100.
And, the number comes before 100 is 99.

Therefore, if we squaring 99, we get the largest four digit perfect square.

So, the largest four digit perfect square is 9801.

Rough Workspace:

Example #9

Find the smallest number which when multiplied with 8820, the product became a perfect square.

A. 2

B. 3

C. 5

D. 7

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Correct Answer is: 5 [Option C].

How to Solve:
So, to solve this question we need to arrange the number 8820 in such manner, so that we can find the smallest multiplicand.

Therefore, we can say that,
8820
or, 2 x 2 x 3 x 3 x 5 x 7 x 7
or, 2² x 3² x 5 x 7²

Therefore, every multiplicand here is a perfect square, except 5.
So, if we multiply 8820 by 5, the product became a perfect square.

2² x 3² x 5 x 5 x 7²
= 2² x 3² x 5² x 7²
= 44100 this is a perfect square

Rough Workspace: