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. 9

B. 0.9

C. 0.09

D. 0.009

How to Solve:

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

Now, as you can see that the sum of decimal places for both numerator and denominator is same. So, we can remove that.

Therefore,


or,

or,

so,

finally,

Therefore, the value of the given statement is 0.9.

Example #2

If and , then find the value of:

A. 22

B. 26

C. 30

D. 34

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,

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,

or,

finally,

Therefore, the vale of the given equation is 34.

Example #3

Find the value of:

A. 15

B. 18

C. 21

D. 23

How to Solve:

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

Therefore, the value would be,


or,

or,

so,

or,

finally,

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

Example #4

What will be the unit's place digit of ?

A. 125

B. 128

C. 131

D. 133

How to Solve:
So, to find the unit place digit, we need to find the square root of the give value.

Now, the given number is, 17161.
As we know that,
1. If a perfect square ends with a 1, then the unit’s digit of it's square root has to be either 1 or 9.
2. If a perfect square ends with a 4, then the unit’s digit of it's square root has to be either 2 or 8.
3. If a perfect square ends with a 5, then the unit’s digit of it's square root is definitely 5.
4. If a perfect square ends with a 6, then the unit’s digit of it's square root has to be either 4 or 6.
5. If a perfect square ends with a 9, then the unit’s digit of it's square root has to be either 3 or 7.

Now, in the given number we can see that the number is ending with 1. So, the unit's place digit of the square root has to be either 1 or 9.

As we can see that, no other options, except 131, is ending with either 1 or 9. So, the square root of is 131.

Example #5

Find the square root of:

A. 2

B. 3

C. 4

D. 5

How to Solve:
So, to find the square root of the given equation, we need to arrange it properly.

Therefore,


or, applying the formula of a² - b²

or,

so,

finally,

Therefore, the square root of is 3.

Example #6

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.

Example #7

If, , then find the value of n.

A. 5

B. 6

C. 7

D. 8

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.

Example #8

How to Solve:
So, to find the rational square root, we need to find the square root of every option given in the question.

Therefore,


or,

or, which is not rational

Now,


or,

or, which is not rational

Then,


or,

or, which is rational

Finally,


or,

or, which is not rational

Therefore, from our evaluation, we can clearly say that the option value 0.09 has a rational square root.

Example #9

Example #10

How to Solve:
So, to find the required number, we need to arrange it into an equation.

Let, the number be X.
Therefore, we can say,


or,

or,

so,

or,

finally,

Therefore, the number is 231.

If you need any farther help on fractional Square root, then let us know. We will discuss on those problems here in www.AptitudeTricks.com.