Short cut tricks to find square root and cube root of a number

CUBE ROOT OF A NUMBER

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).

cube roots unit digits

Now look at the image 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.

 

#2. DERIVING CUBE ROOT FROM REMAINING DIGITS

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

Q. 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 474552 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 ten’s digit of the cube root will definitely be 7

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

 

Let us take another example.

Q. 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, 63 < 250 < 73, So tens digit will be 6

So we find cube root of the number to be 63.

 

Here are some more examples.

Q. Simplify: 970299 = ?

Unit digit of number is 9

∴ Unit digit of cube root will be 9

Now we will consider 970

Since, 93 < 970 < 103

So, we find cube root of the number to be 99.
Let’s take another example to make this trick clearer to you.

Q. Simplify: 140608 = ?

Unit digit of number is 8

∴ Unit digit of cube root will be 2

Now we will consider 140

Since, 53 < 140 < 63

So, we find cube root of the number to be 52.

SQUARE ROOT OF A NUMBER

Unit Digits of Squares

First we need to remember unit digits of all squares from 1 to 10. The figure below shows the unit digits of the squares.

sqrt1

Now from the picture we can say that, whenever the unit digit of a number is 9, unit digit of the square root of that number will be definitely 3 or 7. Similarly, this can be applied to other numbers with different unit digits.How to Find Square Root of a Four Digit Number

Let’s learn how to find square root by taking different examples.

Example: Find the square root of 4489.

We group the last pair of digits, and the rest of the digits together.

Now, since the unit digit of 4489 is 9. So we can say that unit digit of its square root will be either 3 or 7.

sqrt2

Now consider first two digits i.e. 44. Since 44 comes in between the squares of 6 and 7 (i.e. 62 < 44 < 72), so we can definitely say that the ten’s digit of the square root of 4489 will be 6.  So far, we can say that the square root will be either 63 or 67.

Now we will find the exact unit digit.

To find the exact unit digit, we consider the ten’s digit i.e. 6 and the next term i.e. 7.

Multiply these two terms

sqrt3

Since, 44 is greater than 42. So square root of 4489 will be the bigger of the two options i.e. 67.
Let us take another example.

Example: What is the square root of 7056?

sqrt4

Unit digit will be 4 or 6.

Since, 82 < 70 < 92

So the square root will be either 84 or 86.

Now consider 8 and 9

sqrt5

Since, 70 is less than 72. So square root will be the lesser of the two values i.e. 84.

Let’s try it out with five digit numbers now!

How to Find Square Root of a Five Digit Number

We pair the digits up starting from the right side. Since there is one extra left over after two pairs are formed, we club it with the pair closest to it.

Example: √(16641) = ?

sqrt6

Unit digit will be 1 or 9.

Since, 122 < 166 < 132

So, the square root will definitely be 121 or 129.

Now, consider 12 and 13

sqrt7

Since, 166 is greater the 156, we pick the larger of the options i.e. 129.

 

Let’s take another example, so that this trick will be clear to you.

Example: √(33489) = ?

sqrt8

Unit digit will be 3 or 7.

Since, 182 < 334 < 192

So, square root will be 183 or 187.

Now consider 18 and 19.

sqrt9

Now, 334 is less than 342. So, the square root will be lesser of the two numbers i.e. 183.

The cube root of .000216 is:

What should come in place of both x in the equation x / √128=√162 /x

(1.5625)^(1/2) = ?

The square root of (7 + 3√5) (7 - 3√5) is

(√625 x 14 x 11 / 11 x √25 x √196

Leave a Reply

Your email address will not be published. Required fields are marked *