Quantitative Aptitude

Solving Square Root is a child’s play now

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

**Square Roots of four-digit number (For Perfect Squares):**

## 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.

**Square Root of Five Digit Number (For Perfect Squares):**

**Square Root of Five Digit Number (For Perfect Squares):**

## 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

- 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**.

- 9 will be your first digit of the answer.
- Square Root of 0925 becomes 95.

**Square Root of Six Digit Number(For Perfect Squares):**

**Square Root of Six Digit Number(For Perfect Squares):**

## 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.