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

## APC Understanding Mathematics Chapter-3 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**

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**

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**

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**

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**

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**

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**

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**

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 :**

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 :**

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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