By what least number should we multiply 1008 to make it a perfect square?a)8b)7c)2d)5Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Yes By dividing by 7 we will get 1008/7=144....so here 144 as a perfect square of 12..

Answer

First prime factorise 1008.

You will get 2 x 2 x 2 x 2 x 3 x 3 x 7

a^2=a x a

So, make pairs from the prime factorisation of 1008.

So, you will get 2 pairs of 2 and 1 pair of 3.

However, 7 doesn't make a pair. So, 1008 x 7 = perfect square

Answer

7

Answer

Solution:
Let's factorize 1008 into its prime factors.
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
To make a perfect square, we need each prime factor to have an even exponent.
We have two 2's and two 3's, so we need one more 2 and one more 3.
Thus, the smallest whole number by which 1008 should be multiplied to get a perfect square number is:
2 x 2 x 2 x 2 x 3 x 3 x 7 x 2 x 3 = 2^4 x 3^2 x 7
This is equal to (2 x 3)^2 x 7, which is a perfect square.
Therefore, the correct answer is option 'B', which is 7.

Answer

A

Similar Quant Doubts

By what least number should we multiply 1008 to make it a perfect square?

Which least number should be subtracted from 629 so as to get a perfect square ?

Find the least square number (perfect squar e) which is exactly divisible by each of the numbers 6, 9, 12

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company