# (Online Course) CSAT Paper - II : Basic Numeracy: Square Root & Cube Root

## Basic Numeracy

## Square Root & Cube Root

A Civil Servant should be well-versed in concepts of Square Root & Cube Root. In the Civil Services Aptitude Test Paper 2, in Basic Numeracy, certainly there will be asked some questions fromsquare roots and cube roots of number to test fast calculation skills of a candidate.

## Square Root

The square root of a number is that number the product of which itself gives the given number, ie, the square root of 400 is 20, the square root of 625 is 25.

The process of finding the square root is called evaluation. The square root of a number is denoted by the symbol Ö called the radical sign. The expression “ Ö9 ” is read as “root time”, “radical nine” or “the square root of nine”.

## How to Find the Square Root of an Integer?

**(i) By the method of Prime Factors:** When a given number is a perfect
square, we resolve it into prime factors and take the product of prime factors,
choosing one out of every two.

**Example 1:** Find the square root of 4356.

**Solution.**

**Thus from the above example it is clear that in order to
find the complete square root of a given number every prime factor of that
number should be repeated twice. Thus, we can make a number which is not a
perfect square, a perfect square by multiplying or dividing the number by those
factors of it which are not contained in pairs.**

**Example 2:** Find the least number by which 1800 be multiplied or
divided to make it a perfect square.

**Solution.** 1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5

The least number by which the given number be multiplied or divided is 2.

**(ii) By the method of Long Division:** This method can be used when the
number is large and the factors cannot be determined easily. This method can
also be used when we want to add a least number or to subtract a least number
from a given number so that the resulting number may give a perfect square of
some number.

**Example 3:** Find the square root of 156816.

**Solution.**

**Explanations:** Firstly, mark off the digits in pairs starting from the
unit’s digit. Each pair is called a period.

Now, 32 = 9 and 42 = 16. So we take 32 = 9 and on subtracting 9 from 15 we get 6
as remainder.

Now, bring down the next period ie,

Now, double the root figure already found which is 3 and write it to the left.

Now, from trial and error we find 69 × 9 = 621 which is closet and least to 668.
So, place 9 to right of 6 changing it to 69. We also put another 9 to the right
of the quotient 3 making it 39. Now, we subtract 621 from 668. We get a
remainder of 47.

Now, repeat the whole process till there is no period left over to be brought
down

**To Find the Square Root of a Fraction**

**To Find the Cube Root of a Decimal**

**Example 12:** Find the cube root of 19.683.

**To Find the Cube Root of Fraction**