NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.4 Part 5

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Image shows the square root of the number to get quotient an …

Image Shows the Square Root of the Number

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

Image shows the square root of the number 402 and remainer

Image Shows the Square Root of the Number 402 and Remainer

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

Image shows the square root of the number 400

Image Shows the Square Root of the Number 400

i.e

Hence, the square root of 400 is 20.

(ii) 1989

Image shows the square root of the number 1989 and remainer

Image Shows the Square Root of the Number 1989 and Remainer

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

Image shows the square root of the number 1936

Image Shows the Square Root of the Number 1936

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.

Image shows the square root of the number 3250 and remainer

Image Shows the Square Root of the Number 3250 and Remainer

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

i.e 7

Image shows the square root of the number 3249

Image Shows the Square Root of the Number 3249

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.

Image shows the square root of the number 825 and remainder

Image Shows the Square Root of the Number 825 and Remainder

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

i.e

Image shows the square root of the number 784

Image Shows the Square Root of the Number 784

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.

Image shows the square root of the number 4000 and remainder

Image Shows the Square Root of the Number 4000 and Remainder

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

Image shows the square root of the number 3969

Image Shows the Square Root of the Number 3969

Hence, the square root of 3969 is 63.