Find the least number that must be added to $1300$ so as to get a perfect square. Also find the square root of the perfect square.

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Solution

We can find $\sqrt{1300}$ by long division method and the remainder is $4$

This shows that $36^{2} < 1300$

Next perfect square number is $37^{2} = 1369$

Hence the number to be added is $37^{2} - 1300 = 1369 - 1300 = 69$

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Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

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Find the least number that must be added to 1300 so as to get a perfect square. Also find the square root of the perfect square.

We can find √1300 by long division method and the remainder is 4This shows that 362<1300Next perfect square number is 372=1369Hence the number to be added is 372−1300=1369−1300=69

Find the least number that must be added to $1300$ so as to get a perfect square. Also find the square root of the perfect square.

We can find $\sqrt{1300}$ by long division method and the remainder is $4$

This shows that $36^{2} < 1300$

Next perfect square number is $37^{2} = 1369$

Hence the number to be added is $37^{2} - 1300 = 1369 - 1300 = 69$