Question

10.The least number to be multiplied by each of 4,9 and 10 to make product a perfect square is​

Answer 1

Given:

4,9 and 10 to make product a perfect square

To find:

The least number to be multiplied by each of 4,9 and 10 to make product a perfect square

Solution:

The given numbers are:

4 = 2 × 2

9 = 3 × 3

10 = 2 × 5

⇒ 2 × 2 × 3 × 3 × 2 × 5 = 2³ × 3² × 5 = 8 × 9 × 5 = 360

360 × 2 = 720 not a perfect square

360 × 3 = 1080 not a perfect square

360 × 4 = 1440 not a perfect square

360 × 5 = 1800 not a perfect square

360 × 6 = 2160 not a perfect square

360 × 7 = 2520 not a perfect square

360 × 8 = 2880 not a perfect square

360 × 9 = 3240 not a perfect square

360 × 10 = 3600  a perfect square

we need to multiply 360 by 10 to get a perfect square

360 × 10 = 3600 = 60²