Question

find the smallest number that must be subtracted from 856 to make it prefect square ​

Answer 1

Answer:

15 must be subtracted from 856 so that we gets a number which is a perfect square number that is 841 which a square root of 29...

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Answer 2

The smallest number is 15; that must be subtracted from 856 to make it perfect square.

Given:

• 856

To find:

• find the smallest number that must be subtracted from 856 to make it prefect square .

Solution:

Step 1:

Take square root of 856.

$\: \: \: 2 |8 \: \: 56|29.2 \\ + 2 |4 \: \: \: \: \: \: | \: \: \: \\ - - - - - \\ 49|456| \\ + 9|441| \\ - - - - - \\ 582 |1500 | \\ + 2 |1164| \\ - - - -$

and so on.

It is clear that it would be the complete square of 29, if something least will be subtracted.

Step 2:

Find the square of 29.

${29}^{2} = 841$

So,

$856 - 841 = 15$

Atleast we have to subtract 15 to convert 856 to be a perfect square.

Step 3:

Verification.

$\: \: \: 2 |8 \: \: 41|29 \\ + 2 |4 \: \: \: \: \: \: | \: \: \: \\ - - - - - \\ 49|441| \\ \: \: \: \: \: |441| \\ - - - - - \\ 0 \\ - - - - - -$

Thus,

The smallest number is 15; that must be subtracted from 856 to make it prefect square.

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