# NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.4 Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question: 4** Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

(i) 402

(ii) 1989

(iii) 3250

(iv) 825

(v) 4000

**Answer**:

(i) 402

Here, the remainder is 2.

We know that, if we subtract the remainder from the number we get a perfect square.

Therefore 2 must be subtracted from 402 to get a perfect square

i.e.

Hence, the square root of 400 is 20.

(ii) 1989

We know that, if we subtract the remainder from the number, we get a perfect square.

Therefore 44 must be subtracted from 1989 to get a perfect square

i.e. = 44

Hence, the square root of 1936 is 44.

(iii)

Given, 3250

We know that, if we subtract the remainder from the number we get a perfect square.

Therefore 1 must be subtracted from 3250 to get a perfect square

i.e. 7

Hence, the square root of 3249 is 57.

(iv) 825

Give, 825

We know that, if we subtract the remainder from the number, we get a perfect square.

Therefore 41 must be subtracted from 825 to get a perfect square.

i.e.

Hence, the square root of 784 is 28.

(v) 4000

Given, 4000

We know that, if we subtract the remainder from the number,

we get a perfect square.

Therefore 31 must be subtracted from 4000 to get a perfect square

Hence, the square root of 3969 is 63.