ML Aggarwal Squares and Squares Roots Exe-3.1 Class 8 ICSE Ch-3 Maths Solutions

ML Aggarwal Squares and Squares Roots Exe-3.1 Class 8 ICSE Ch-3 Maths Solutions. We Provide Step by Step Answer of  Exe-3.1 Questions for Squares and Squares Roots as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-8.

ML Aggarwal Squares and Squares Roots Exe-3.1 Class 8 ICSE Maths Solutions

Board ICSE
Publications Avichal Publishig Company (APC)
Subject Maths
Class 8th
Chapter-3 Squares and Squares Roots
Writer ML Aggarwal
Book Name Understanding
Topics Solution of Exe-3.1 Questions
Edition 2023-2024

Squares and Squares Roots Exe-3.1

ML Aggarwal Class 8 ICSE Maths Solutions

Page-47

Question 1. Which of the following natural numbers are perfect squares? Give reasons in support of your answer.

(i) 729
(ii) 5488
(iii) 1024
(iv) 243

Answer :

(i) 729

Which of the following natural numbers are perfect squares? Give reasons in support of your answer.

729 = 3 × 3 × 3 × 3 × 3 × 3

729 is the product of pairs of equal prime factors

Hence, 729 is a perfect square.

(ii) 5488

Which of the following natural numbers are perfect squares? Give reasons in support of your answer.

5488 = 2 × 2 × 2 × 2 × 7 × 7 × 7

After pairing the same prime factors, one factor 7 is left unpaired.

Hence, 5488 is not a perfect square.

(iii) 1024

Which of the following natural numbers are perfect squares? Give reasons in support of your answer.

1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

After pairing the same prime factors, there is no factor left.

Hence, 1024 is a perfect square.

(iv) 243

Which of the following natural numbers are perfect squares? Give reasons in support of your answer.

243 = 3 × 3 × 3 × 3 × 3

After pairing the same prime factors, factor 3 is left unpaired.

Hence, 243 is not a perfect square.

Question 2. Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number.

(i) 1296
(ii) 1764
(iii) 3025
(iv) 3969

Answer :

(i) 1296

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number.

1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

After pairing the same prime factors, no factor is left.

Hence, 1296 is a perfect square of 2 × 2 × 3 × 3 = 36.

(ii) 1764

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number.

1764 = 2 × 2 × 3 × 3 × 7 × 7

After pairing the same factors, no factor is left.

Hence, 1764 is a perfect square of 2 × 3 × 7 = 42.

(iii) 3025

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number.

3025 = 5 × 5 × 11 × 11

After pairing the same prime factors, no factor is left.

Hence, 3025 is a perfect square of 5 × 11 = 55.

(iv) 3969

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number.

3969 = 3 × 3 × 3 × 3 × 7 × 7

After pairing the same prime factors, no factor is left.

Hence, 3969 is a perfect square of 3 × 3 × 7 = 63.

Question 3. Find the smallest natural number by which 1008 should be multiplied to make it a perfect square.

Answer :

Find the smallest natural number by which 1008 should be multiplied to make it a perfect square.

1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7

After pairing the same kind of prime factors, one factor 7 is left.

Now multiplying 1008 by 7

We get a perfect square

Hence, the required smallest number is 7.

Question 4. Find the smallest natural number by which 5808 should be divided to make it a perfect square. Also, find the number whose square is the resulting number.

Answer :

Find the smallest natural number by which 5808 should be divided to make it a perfect square. Also, find the number whose square is the resulting number.

5808 = 2 × 2 × 2 × 2 × 3 × 11 × 11

After pairing the same kind of prime factors, factor 3 is left.

Now dividing the number by 3, we get a perfect square.

Hence, the square root of the resulting number is 2 × 2 × 11 = 44.

—  : End of ML Aggarwal Squares and Squares Roots Exe-3.1 Class 8 ICSE Maths Solutions :–

Return to –  ML Aggarwal Maths Solutions for ICSE Class -8

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