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**1. Square Root**

If x^{2} = y, we say that the square root of y is x and we write âˆšy = x.

Thus, âˆš4 = 2, âˆš9 = 3, âˆš196 = 14.**2. Cube Root**

The cube root of a given number x is the number whose cube is x.

we, denote the cube root of x by 3âˆšx.

Thus,**(a)****(b)****EASY TRICKS TO FIND SQUARE ROOTS AND CUBE ROOTS**

To find square root or cube root of a number is not an easy task. When youâ€™re giving a time-bound exam like CAT, CMAT, CET, NMAT, etc. this can drain you of your precious time. This is a worse deal when finding square or cube root is only part of a bigger problem, like in Data Interpretation or Compound Interest problems in Quantitative Aptitude.

So if your Mental Mathematics is a little weak, let us learn how to quickly and easily find square root or cube root of a number. This trick is sure to save you at least 40 seconds of calculations per question. At first you will find it difficult but with practice, you will be able to find square root or cube root of any number. Then let us start.**FINDING SQUARE ROOT**

Above 100:

103^{2} = 10609**Step 1:** Add the number to the ones digit:

103 + 3 = 106**Step 2:** Square the ones digit number (if the result is a single digit put a 0 in front of it):

3^{2} = 09**Step 3:** Place the result from Step 2 next to the result from Step 1: 10609

Below 100:

97^{2} = 9409**Step 1:** Subtract the number from 100: 100- 97 = 3**Step 2:** Subtract the number (from Step 1) from original number : 97-3 =94**Step 3:** Square the result from Step 1 (if the result is a single digit put a 0 in front of it): 3^{2} = 09**Step 4:** Place the result from Step 3 next to the result from Step 2: 9409

Below 50:

48^{2} = 2304**Step 1:** Subtract the number from 50: 50-48=2**Step 2:** Subtract the result (from Step 1) from 25: 25-2 =23**Step 3:** Square the result from Step 1 if the result is a single digit put a 0 in front of it ) : 2^{2} = 04**Step 4: **Place the result from Step 3 next to the result from Step 2: 2304

Above 50:

53^{2} = 2809**Step 1:** Add 25 to the ones digit: 25 + 3 = 28**Step 2: **Square the ones digit number (if the result is a single digit put a 0 in front of it ) : 3^{2} = 09**Step 3:** Place the result from Step 2 next to the result from Step 1 : 2809**FINDING CUBE ROOT****Remembering Units Digits**

First we need to remember cubes of 1 to 10 and unit digits of these cubes. The figure below shows the unit digits of cubes (on the right) of numbers from 1 to 10 (on the left).

1 = 1

2 = 8

3 = 7

4 = 4

5 = 5

6 = 6

7 = 3

8 = 2

9 = 9

10 = 0

Now with reference to above we can definitely say that:

Whenever unit digit of a number is 9, the unit digit of the cube of that number will also be 9. Similarly, if the unit digit of a number is 9, the unit digit of the cube root of that number will also be 9. Similarly, if unit digit of a number is 2, unit digit of the cube of that number will be 8 and vice versa if unit digit of a number is 8, unit digit of the cube root of that number will be 2. Similarly, it will be applied to unit digits of other numbers as well.**DERIVING CUBE ROOT FROM REMAINING DIGITS**

Letâ€™s see this with the help of an example. Note that this method works only if the number given is a perfect cube.

Find the cube root of 474552.

Unit digit of 474552 is 2. So we can say that unit digit of its cube root will be 8.

Now we find cube root of 447552 by deriving from remaining digits.

Let us consider the remaining digits leaving the last 3 digits. i.e. 474.

Since 474 comes in between cubes of 7 and 8.

So the tenâ€™s digit of the cube root will definitely be 7

i.e. cube root of 474552 will be 78.

Let us take another example.

Find the cube root of 250047.

Since the unit digit of the number is 7, so unit digit in the cube root will be 3.

Now we will consider 250.

Since, 6^{3} < 250 < 7^{3}, So tens digit will be 6

So we find cube root of the number to be 63.**FOR NUMBERS BETWEEN 25 - 50**

Time saving techniques are paramount when we have to deal with Quant questions in any competitive exams, which is missing a place in the provided material.

Many a times we need to find a square of a number and it gets difficult to remember it beyond 30. So, here is a trickâ€¦..

Suppose, we need to find the square of 47.**Step 1:** If the number is between 25 and 50.

Find out by how much the given number is smaller than 47. In the above case, it is 3.**Step 2:** Write the square of this number in unitâ€™s and tenâ€™s place in this manner Square of 3 is 9.

It is a single digit number, so we can write it as 09**Step 3:** Find the difference between the given number and 25

47-25 = 22

Therefore, square of 47 will be 2209.

This is true for the square of any number between 25 and 50.**FOR NUMBERS BETWEEN 51 - 75****Example: Square of 73 ****Step 1:** find the difference between the number (73) and 50, which is 23.**Step 2: **Find the square of the difference, 23^{2} = 529. Keep the last two number aside which will be the last two digits of the square of 73.**Step 3:** Find the difference between the number for which we have to find the square and add the difference with 5(which is the first digit of the square of the difference)

â‡¨ (73 - 25) + 5 = **53**. This number will be the first two digits of the square.

The square of the number 73 will be = 5329**FOR NUMBERS BETWEEN 76 - 100****Example: Square of 88****Step 1:** Subtract the number from 100.. (100 - 88 = 12)**Step 2:** Find the square of the number obtained .. 12^{2 }= 144

Last two digits of the square of this number will be last 2 digits of square of 88.**Step 3:** The first two digits will be obtained by adding the first digit of square of 12. i.e. 1 and the difference between 88 and 12 (88 - 12 = 76)

76 + 1 = 77

The square of the number 88 will be = 7744

Square of 87 = (87 - 13)â€¦â€¦.13^{2}

74â€¦â€¦â€¦â€¦â€¦.69

7569

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