Question

A No.
8. By what least number should we multiply the following to make it a perfect square?
(b) 3456
(a) 700
Last number should we al
cat sa​

Answer 1

By what least number should we multiply the following to make it a perfect square?

We know that:

• The number whose each of the prime factors are in pair is known as perfect square.
• To make a number as perfect square, we have to make each of its prime factors in a pair.

a) 700

By prime factorisation.

Factors of 700 = 2 × 2 × 5 × 5 × 7

If we multiply 7 with 700 then it will become perfect square.

• Perfect square = 700 × 7 = 4900
• Square root = √4900 = 70

Hence,

• 7 should be multiply with 700 to make it a perfect square.

b) 3456

By prime factorisation.

Factors of 3456 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

If we multiply 2 and 3 with 3456 then it will become perfect square.

• Perfect square = 3456 × 2 × 3 = 20736
• Square root = √20736 = 144

Hence,

• 6 should be multiply with 3456 to make it a perfect square.

Answer 2

Given :-

700

3456

To Find :-

Number to be added

Solution :-

Formula :-

At first we will find the prime factors of the given number and then we will pair them. If one number is left then the number should be multiplied and if 2 number left then we will multiply them.

1. 700

(2 × 2) × (5 × 5) × 7

So,

We need to pair them

We left with 7. 7 must be multiply

2. 3456

2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

Pair them

(2 × 2) × (2 × 2) × (2 × 2) × 2 × (3 × 3) × 3

2 × 3

6

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