Square Roots Of Perfect Squares

You May have some knowledge about this trick. But not completely.

To find the square roots it is necessary to be well versed with the squares of the numbers from 1 to 10.

The squares are given below. Memorize them before proceeding ahead.

On the basis of observation of unit digits, we can form a table as given below:

Note: ‘A perfect square will never end with the digits 2, 3, 7 or 8’

Let's know the trick by solving some questions.

Q.Find the square root of 7744?

A.

• The number 7744 ends with 4. Therefore the square root ends with 2 or 8. The answer at this stage is __2 or__8.

• Next, we take the complete number 7744. We find that the number 7744 lies between 6400 (which is the square of 80) and 8100 (which is the square of 90).

The number 7744 lies between 6400 and 8100. Therefore, the square root of 7744 lies between the numbers 80 and 90.

• From the first step we know that the square root ends with 2 or 8. From the second step we know that the square root lies between 80 and 90. Of all the numbers between 80 and 90 (81, 82, 83, 84,85, 86, 87, 88, 89) the only numbers ending with 2 or 8 are 82 or 88. Thus, out of 82 or 88, one is the correct answer.

(Answer at this stage is 82 or 88)

• Observe the number 7744 as given below:

Is it closer to the smaller number 6400 or closer to the bigger number 8100 ?

If the number 7744 is closer to the smaller number 6400 then take the smaller number 82 as the

answer. However, if it is closer to the bigger number 8100, then take 88 as the answer.

In this case, we observe that 7744 is closer to the bigger number 8100 and hence we take 88 as the

answer.

The square root of 7744 is 88.

Q.Find the square root of 2304?

A.

• 2304 ends in 4 and so the root either ends in a 2 or in a 8

• 2304 lies between 1600 and 2500. So, the root lies between 40 and 50.

• Thus, the two possibilities are 42 and 48.

• Lastly, the number 2304 is closer to the bigger number 2500. Hence, out of 42 and 48 we take the bigger number 48 as the correct answer.

Q.Find the square root of 5184 ?

A.

• 5184 ends in 4. So the square root ends in either 2 or 8 (Answer = ____2 or ____8)

• 5184 is between 4900 and 6400. So the square root is between 70 and 80. Combining the first two steps, the only two possibilities are 72 and 78

• Out of 4900 and 6400, our number 5184 is closer to the smaller number 4900 (70 × 70). Thus, we take the smaller number 72 as the correct answer

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