Question

what is the the smallest number that can be multiplied to 3200 to give a perfect square?​

Answer 1

Answer:

0 is the correct answer.

Answer 2

Given:

Number to be multiplied with = 3200

To find:

The smallest number multiplied with 3200 for a perfect square.

Solution:

When a number is multiplied with itself, the product obtained is called perfect square. 1, 4, 9, 16... are the perfect squares of 1, 2, 3, 4.... respectively.

Here, we need to find a number when multiplied with 3200 should give a perfect square. Finding the factors of 3200

$3200=2*2*2*2*2*2*2*5*5$

There are three pairs of 2 and one pair of 5 with one 2 remaining. When we multiply 3200 with 2, we get four pairs of 2 and hence the resultant will be 6400 which is a perfect square.

∴ $3200*2=(2*2)*(2*2)*(2*2)*(2*2)*(5*5)$  

$\sqrt{ 3200*2}=\sqrt{(2*2)*(2*2)*(2*2)*(2*2)*(5*5)}$

$\sqrt{3200*2}=2*2*2*2*5=80$

2 is the smallest number to be multiplied with 3200 in order to give a perfect square.