Square Root and Cube Root Shortcut Method

Learn the shortcut to find square root and cube root in just few seconds from our simple step by step tutorial. The most important thing in working out this shortcut is to remember the square of the numbers between 1 to 25 and cubes of numbers between 1 to 15. By memorizing this tables you can easily perform the shortcut which would help you out in scoring better in the examination. Here we have shared the square root and cube root short tricks with examples.

Square Root and Cube Root Short Tricks

Example for Square Root Shortcut

Find Square Root of 729.

Step 1:

First pair the digits in the number from its right.

7 29

Step 2:

Find the ten's place digit of the result of square root number (i.e) 729. To find the ten's place, find the nearest square of the first grouped pair from left
Here, nearest square of 7 is √4. (Take the smallest square root) Square Root of 4 is 2. Hence, the ten's digit of Square root of 729 is 2 .

Step 3:

Now find the unit's place digit of the result of square root number . To find the unit's digit, remember the below note. This shows unit digits of all squares from 1 to 10.

Note:

If Unit Number Ends In Unit Digits of Squares
11 or 9
42 or 8
64 or 6
93 or 7
55
00

Here, unit digit is 9 and hence square root of 729 unit digit will be either 3 or 7.

Step 4:

To find the unit's digit, follow the steps below: Step 4.1 Multiply the ten's place digit of square root of 729 (i.e) 2 with its consecutive number. 2 x 3 = 6. Step 4.2 Compare the result obtained with the first pair of the original number (729) from left (i.e) 7.

Note:

1. If the first pair of the original number > Result obtained on multiplication, then unit place will be the greatest number.
2.If the first pair of the original number < Result obtained on multiplication, then unit place will be the least number.

Step 4.3 Here, first pair of the original number > Result obtained on multiplication (i.e) 7 > 6. Hence, the unit place is 7. Therefore, Square Root of 729 is 27.

Example for Cube Root Shortcut

Find Cube Root of 13824.

Note:

To find the unit place of the cube root, remember the following points. 1.If the Last digit of a cube root is 8 than the unit digit will be 2.
2.If the Last digit of a cube root is 2 than the unit digit will be 8.
3.If the Last digit of a cube root is 3 than the unit digit will be 7.
4.If the Last digit of a cube root is 7 than the unit digit will be 3.
5.If the Last digit of a cube root is other than 2,3,7,8 then the unit digit will be the same digit.

Step 1:

Here, the last digit of 13824 is 4, therefore unit place of cube root is 4.

Step 2:

Now strike the last 3 digits of the given number.
13824

Step 3:

Now, find the nearest cube root of the first 2 digit from the left (i.e) 13. Therefore, the nearest cube root of 13 is 8. (i.e) 23 is 8

Step 4:

Now, it is found that ten's place digit is 2.Therefore, Cube root of 13824 is 24.

This square root and cube root short tricks tutorial page helps you to increase your problem-solving speed by teaching you this useful square root and cube root shortcut method.


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