Question

which is the smallest number that can be multiplied to 7920 to give a perfect square

Answer 1

Find the prime factors:

7920 = 2⁴ x 3² x 5 x 11

Define k:

k is the number that is needed to multiply

Solve k:

7920 = 2⁴ x 3² x 5 x 11

To be a perfect square, the exponent must be in multiples of 2s7920 = 2⁴ x 3² x 5 x 11

7920k = 2⁴ x 3² x 5² x 11²

Therefore k = 5 x 11 = 55

Answer: the smallest number that be multiplied to 7920 is 55

Answer 2

Answer:

55

Step-by-step explanation:

Given to find  the smallest number that can be multiplied to 7920 to give a perfect square.

 Now first find the prime factors of the given number 7920.

 We get the factors as 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11. here we notice the underlined numbers are in pairs. To make it square we need to multiply the other two numbers also equal, so we multiply by 5 and 11.

So 5 x 11 = 55. hence we have to multiply the given number by 55  which will be equal to 7920 x 55 = 435600 which is a perfect square.