Quantitative Aptitude
Solving Square Root is a child’s play now shikha
August 14, 2015

Finding the Square Root of two or three-digit numbers is the easiest of all but when digits go on adding, we feel fearsome how to solve the puzzle within a second or two. Friends! If you are in a similar situation where you have a long mathematical puzzle in which square root is just a part of it then let me take you out of this agony.

Here we go….First of all, go through these important facts:

• Number ending with 2,3,7,8 will never give you a perfect square.
• Number ending with an odd number of Zeros again has no perfect square.

Let’s try to solve the Square Root with the simplest method

## Question1: √ 1024

Solution: Steps to solve:

• Break the number into two halves i.e. 10 and 24
• Take the second half i.e. 24 and check extreme last digit 4 appearing in the table:
• The extreme last digit 4 is coming after the squaring of 2 and 8.This indicates that the answer will contain the last digit from these options 2 and 8.
• Now take the first half i.e. 10 and check the table again.
• Now check first half 10 lies in squares and choose the smaller value always.
• From 3 and 4, 3 is smaller and becomes the first digit of your answer.
• Now we have options of first and last digit of answer 32 or 38.
• To find out the right option multiply 3 and 4.
• Given 10<12 b=""> so choose the smaller option 32.
• Square Root of 1024 is 32.

## Question2: √ 2116

Solution:

• Break into two halves 21 and 16
• Take the second half and check extreme digit 6 appearing in the same table. This indicated that the answer will contain the last digit from these two 4 and 6.
• Now take the first half i.e. 21 and again check the table.
• Now check first half 21 lies in squares and choose lower value always.
• From 4 and 5, 4 is smaller and become the first digit of your answer.
• First and last digit options of answers 44 and 46.
• To find out the right option multiply 4 and 5
• Given 21>20 so we choose greater value i.e. 46.
• Square Root of 2116 is 46.

## Question1: √ 13456

Solution:

• Break into two halves such that you always left with two digits in the second half.

134      56

• Repeat steps 2 and 3 again.
• 6 appear in 4 and 6 and become options of answer’s last digit.
• Now take first halve. The table is extended as we have now the first half containing three digits.
• Now check first half 134 lies in squares and choose lower value always.
• 11 becomes the first digit of the answer.
• The first and last digit options of the answer are 114 and 116.
• To find out the right option multiply 11 and 12
1. Given 134 >132 so choose greater value i.e.116
• Square Root of 13456 is 116.

## Question2: √ 9025

Solution:

• Break into two halves 90 and 25 such that you always left with two digits in the second half.

90      25

• Second half 25 is a perfect square of 5 so we have only one option of the last digit i.e. 5
• Take 90 and check where it lies and take the lower value always.
• Square Root of 0925 becomes 95.

## Question1: √ 262144

Solution:

• Break into two halves 2621 and 44 such that you always left with two digits in second half.

2621      44

• Check the second half 44 appear in table.
• Last Digit 4 appears at 2 and 8.
• Now take first halve. Table is extended as we have now first half containing four digits .
• Now check first half 2621 lies in squares and choose lower value always.
• 51 becomes first digit of the answer.
• First and last digit options of answer are 512 and 518.
• To find out the right option multiply 51 and 52
• Given 2621 < 2652 so choose smaller value i.e. 512 and is the answer.