Find the least number which must be subtracted from the following numbers to make them a perfect square:
(i) 2361
(ii) 194491
(iii) 26535
(iv) 16160
(v) 4401624

To do:

We have to find the least number which must be subtracted from the given numbers to make them a perfect square.

Solution:

Square root of 2361 is,

Quotient $=48$

Remainder $=57$

Therefore,

To make 2361 a perfect square, we have to subtract 57 from it. 

The least number which must be subtracted from 2361 to make it a perfect square is 57.

(ii) Square root of 194491 is,

Quotient $=441$

Remainder $=10$

Therefore,

To make 194491 a perfect square, we have to subtract 10 from it. 

The least number which must be subtracted from 194491 to make it a perfect square is 10.

(iii) Square root of 26535 is,

Quotient $=162$

Remainder $=291$

Therefore,

To make 26535 a perfect square, we have to subtract 291 from it. 

The least number which must be subtracted from 26535 to make it a perfect square is 291.

(iv) Square root of 16160 is,

Quotient $=127$

Remainder $=31$

Therefore,

To make 16160 a perfect square, we have to subtract 31 from it. 

The least number which must be subtracted from 16160 to make it a perfect square is 31.

(v) Square root of 4401624 is,

Quotient $=2098$

Remainder $=20$

Therefore,

To make 4401624 a perfect square, we have to subtract 20 from it. 

The least number which must be subtracted from 4401624 to make it a perfect square is 20.

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Updated on: 10-Oct-2022

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