MATHS SHORTCUTS

Finding SQUARES & SQUARE ROOTS quickly in exam in necessary.

All you need is first to understand what is squares.

**SQUARE OF NUMBERS ENDING IN 5**

Say 25,

Take the first number which is 2 & increase it by 1 (2+1) is 3.

Multiply these two numbers, 2 x 3 = 6.

Now just add 25 at the end, 6'25'.

So, 25 x 25 is 625.

One more example,

Say 75

first number is 7, increase by 1, so 8.

7 x 8 = 56, add 25 at end.

So, 75 x 75 is 5625.

Try 65, 125, .......

Say 22,

So write 22 as (22 - 2) & (22 + 2),

which is now easy 20 x 24 = 480.

Then take last number which is 2.

Square it which is 4 and just add it to the number.

So 480 + 4 = 484.

One more example,

Say 32,

So write 32 as (32 - 2) & (32 + 2),

which is now easy 30 x 34 = 1020.

Then take last number which is 2.

Square it which is 4 and just add it to the number.

** SQUARE ROOT OF A NUMBER **To find square root of a number, one should be familiar with squares of 1 to 10.

If the given number ends in 1, then square root will end in 1 or 9

If the given number ends in 4, then square root will end in 2 or 8

If the given number ends in 9, then square root will end in 3 or 7

If the given number ends in 6, then square root will end in 4 or 6

__EXAMPLE 1:__

Say, Square root of 1024,

This number ends in 4, so last number should either 2 or 8.

Split the number as 10 / 24.

Then,

Take the first split, which is 10, So 10 lies between square of 3 & 4.

i.e. 9 < 10 < 16, So the first number is 3.

3 ? = 1024, the last number can be 2 or 8 as discussed.

Take the first number which is 3, increase it by 1 i.e 3+1 =4.

So, 3 x 4 =12.

Check if the first number is lesser or greater than 12,

If the first split is greater than 12 then it is 8 & if lesser than 12 then it is 2.

In our case it is 10 which is lesser, so the last number is 2.

3 2 is square root of 1024.

One more example,

**EXAMPLE 2:**

Say, Square root of 9409,

This number ends in 9, so last number should either 3 or 7.

Split the number as 94 / 09.

Then,

Take the first split, which is 94, So 94 lies between square of 9 & 10.

i.e. 81 < 94 < 100, So the first number is 9.

9 ? = 9409, the last number can be 3 or 7 as discussed.

Take the first number which is 9, increase it by 1 i.e 9+1 =10.

So, 9 x 10 =90.

Check if the first split number is lesser or greater than 90,

If the first split is greater than 90 then it is 7 & if lesser than 90 then it is 3.

In our case it is 94 which is greater, so the last number is 7.

9 7 is square root of 9409.

Try to find square root of these, 7569, 5041,......

**PRACTICE, PRACTICE AND PRACTICE A LOT**

**@@@@ HAPPY LEARNING, DO MATHS QUICKER @@@@ **