Class 8 Squares and Square Roots Maths Ex 6.4

NCERT Solutions For Class 8 Maths Chapter 6 Ex 6.4

ncert solutions for class 8 maths chapter 6, Exercise 6.4 involve complete  answers for each question in the exercise 6.4. The solutions provide students a  strategic methods  to prepare for their exam. Class 8 Maths Chapter 8 Squares and Square Roots Exercise 6.4 questions and answers helps students  to perform better in exam and it will  clear doubts definitely. Students will find it extremely easy to understand the questions and learn solving the problems. NCERT Solutions for Class 8 Maths Chapter 8 Squares and Square Roots Exercise 6.4 prepared by our subject matter experts in very delicate, easy and creative way. 

Question 1:

Find the square root of each of the following numbers by division method.

(i) 2304 (ii) 4489 (iii) 3481 (iv) 529 (v) 3249 (vi) 1369 (vii) 5776 (viii) 7921 (ix) 576 (x) 1024 (xi) 3136 (xii) 900

Answer:

Question 2:

Find the number of digits in the square root of each of the following numbers (without any calculation).

(i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625

Question 3:

Find the square root of the following decimal numbers.

(i) 2.56 (ii) 7.29 (iii) 51.84 (iv) 42.25 (v) 31.36

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) The square root of 402 can be calculated by long division method as follows.

The remainder is 2. It represents that the square of 20 is less than 402 by 2.

Therefore, a perfect square will be obtained by subtracting 2 from the given number 402.

Therefore, required perfect square = 402 − 2 = 400

(ii) The square root of 1989 can be calculated by long division method as follows.

The remainder is 53. It represents that the square of 44 is less than 1989 by 53.

Therefore, a perfect square will be obtained by subtracting 53 from the given

number 1989.

Therefore, required perfect square = 1989 − 53 = 1936

(iii) The square root of 3250 can be calculated by long division method as follows.

The remainder is 1. It represents that the square of 57 is less than 3250 by 1.

Therefore, a perfect square can be obtained by subtracting 1 from the given number 3250.

Therefore, required perfect square = 3250 − 1 = 3249

(iv) The square root of 825 can be calculated by long division method as follows.

The remainder is 41. It represents that the square of 28 is less than 825 by 41.

Therefore, a perfect square can be calculated by subtracting 41 from the given number 825.

Therefore, required perfect square = 825 − 41 = 784

And,

(v) The square root of 4000 can be calculated by long division method as follows.

The remainder is 31. It represents that the square of 63 is less than 4000 by 31.

Therefore, a perfect square can be obtained by subtracting 31 from the given number 4000.

Therefore, required perfect square = 4000 − 31 = 3969

Question 5:

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.

(i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412

Answer:

Question 6:

Find the length of the side of a square whose area is 441 m².

Answer:

Question 7:

In a right triangle ABC, ∠B = 90°.

(a) If AB = 6 cm, BC = 8 cm, find AC

(b) If AC = 13 cm, BC = 5 cm, find AB

Answer:

Question 8:

A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

Answer:

It is given that the gardener has 1000 plants. The number of rows and the number of columns is the same.

We have to find the number of more plants that should be there, so that when the gardener plants them, the number of rows and columns are same.

That is, the number which should be added to 1000 to make it a perfect square has to be calculated.

The square root of 1000 can be calculated by long division method as follows.

The remainder is 39. It represents that the square of 31 is less than 1000.

The next number is 32 and 322 = 1024

Hence, number to be added to 1000 to make it a perfect square

= 322 − 1000 = 1024 − 1000 = 24

Thus, the required number of plants is 24.

Question 9:

These are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

Answer:

It is given that there are 500 children in the school. They have to stand for a P.T. drill such that the number of rows is equal to the number of columns.

The number of children who will be left out in this arrangement has to be calculated.

That is, the number which should be subtracted from 500 to make it a perfect square has to be calculated.

The square root of 500 can be calculated by long division method as follows.

The remainder is 16.

It shows that the square of 22 is less than 500 by 16. Therefore, if we subtract 16

from 500, we will obtain a perfect square.

Required perfect square = 500 − 16 = 484

Thus, the number of children who will be left out is 16.