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
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.
Example #2
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 #3
So, to find the square root of the given equation, we need to arrange it properly.
Therefore,
or,
applying the formula of a2 - b2or,
so,
finally,
Therefore, the square root of
is 3.Example #4
and 
, then find the value of:
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 #5
, then find the value of 8 x 32.So, from the question itself we know that,
.Now, we need to find the value of 8 x 32.
Therefore, putting the value in the expression we get,
or,
or,
so,
finally,
So, the value of 8 x 32 is, 56.
Example #6
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 rationalNow,
or,
or,
which is not rationalThen,
or,
or,
which is rationalFinally,
or,
or,
which is not rationalTherefore, from our evaluation, we can clearly say that the option value 0.09 has a rational square root.
Example #7
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 #8
is true?So, to find the value of X, we need to simplify the statement.
Now,
or,
or,
so,
or,
finally,
Therefore, the statement
will be true if the value of X is 62.Example #9
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.
Example #10
So, to find the smallest four digit perfect square, we need to apply some basic math formula.
As, we know the square of 30 is 900. But, it is three digit number. So, the smallest four digit perfect square number should be around 30.
Therefore, we need to apply some basic math formula to find the smallest perfect square.
302 = 900
312 = (30 + 1)2
or, (30)2 + (1)2 + 2x30x1 applying the formula of (a + b)2
or, 900 + 1 + 60
= 961 which is also not four digit number
322 = (30 + 2)2
or, (30)2 + (2)2 + 2x30x2 applying the formula of (a + b)2
or, 900 + 4 + 120
= 1024 which is a four digit number
Therefore, the smallest four digit perfect square is 32.
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.