Question

Find the smallest number by which 700 must be multiplied to make it a perfect square?

Answer 1

Prime Factorisation Of..
700=2×2×5×5×7

Here 7 is not in a Pair.
But 2 and 5 are in Pair.

So 700 multiplied By Seven Will Make it A Perfect square [1400 =70²]

So 7 is the smallest No: by which 700 must be multipled so as to obtain a Perfect Square...


Hope it Helps...
Regards,
Leukonov

Answer 2

Let the smallest number be k

Find the prime factors of 700:

700 = 2² x 5² x 7

For a number to be perfect square, the exponents must be even:

700 = 2² x 5² x 7

700k = 2² x 5² x 7²

∴ k = 7

Answer: the smallest number to make 700 a perfect square is 7.