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# Square Roots and Cube Roots

There are certain topics in a competitive exam that you have to learn in order to the other topics properly. One such topic is Square roots and Cube roots. This topic is important not only because there are direct questions from this topic but it is also important because there are other questions which you can solve easily if you know the square roots and cube roots. Thus, in this article, we will help you with the tips and tricks to solve the roots quickly.

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A number is said to be a square root of another number when it means the criteria of √x = y. You can also denote these numbers as x = y². While the cube is denoted by ³√x. There are some points you need to remember for finding both the roots.

√xy = √x x √y

√(x/y) = √x/√y

= √x/√y x √y/√y = √by/√y

The numbers that are ending with 8 cannot be a square root of any number.

For solving the questions easily in the exam it is important that you remember the square roots and cube roots till 25.

Further, there are certain numbers that have the same unit digits when you square them. They are as below.

• The squares of 2 and 8 will always have 4 as a unit digit.
• Squares of 3 and 7 will have the same unit digit as 9.
• The square of 5 will have a unit digit as 5.
• The squares of 4 and 6 will have unit digit as 6.
• Squares a number with 9 as unit digit will always have 1 as a unit digit.

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Q. Find the square root of 6561.

For the 1st step, ignore the last two digits of this number. Thus, you are left with only 6 and 5.

Now, find a square number which is equal to less than 65. The nearest to this is the number immediately behind 65 which is 64. 64 is a perfect square of number 8. So, the number in the ten’s place will be 8.

Thus, we only need to find the number which is the unit’s place. In this question, the number at unit’s place is 1. So, from the tips given above, you can determine that the number 1 and 9 has 1 as the unit digit while squaring.

So, we need to find the correct number between 1 and 9 for the correct answer.

For this, multiply 8 with the next highest number which is 9. So, the answer is 72. This number is greater than the first two digits of the required number. Thus, you need to take the smaller number between the numbers which is 1.

So, the required number for us is 81.

#### Finding the square root of 5 digit numbers

Q. Suppose the number is 17424.

For this also, start by ignoring the last two digits i.e. 24. Repeat the same procedure for this question. The previous square number here is 169.

So, the number at ten’s place is 13 and we need to find the number between 2 and 8.

Thus, following the previous procedure, you will find that the required answer is 132.

#### How to find the squares of a large number?

Q. Suppose find the square of 47.

Split the numbers given in the question as 4 and 7. Now, you need to use the formula of (x + y)². Instead of x write 4 and instead of y write 7. So, the expansion of (4 + 7)² is 4² + 2 x 4 x 7 + 7². Do not consider the plus sign in between. Thus the three numbers will be 16, 56, and 49.

Now write 9 from 49 and carry forward the remaining 4 to 56. Thus we will get 10 when we add 4 with 6. Thus, write 0 and carry 5 + 1 = 6 to the remaining 16. So, the last digits till now are 09. Again adding 6 with 6 we get 12. So, write down 2 and carry forward the remaining 1. Finally, you have 1 remaining which you carry with 1 which is 2. So, the final answer you get will be 2209.

## Practice Questions

Q. Find the cube root of 5041

A. 65                   B. 69                  C. 71                      D. 79

Q. What is the square root of 12769.

A. 112                 B. 113                C. 115                    D. 117

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