Question

find out the least number by which 7688 should be multiplied so that the resulting number become the perfect square

Answer 1

Hello friend!!

Here's your answer.

Prime factorisation of 7688 is
2 × 2 × 2 × 31 × 31
= 2^3 × 31^2

A number is a perfect square if it's factors have even exponential powers

But here 2 has an odd exponential power

So if we multiply 2 to 7688 it will have even exponential power of both 2 and 31.

Therefore, 2 is the smallest number that must be multiplied to make 7688 a perfect square

HOPE THAT HELPS..... :-)☺️

Answer 2

I am giving the answer step-wise :

Step 1 : Carry out prime factorisation
of 7688
(The factors will be :
2,2,2,31,31)

Step 2 : When you make pairs to find
the square root of 7688 you
find that a 2 is left alone

Step 3 : When you multiply by 2 , it
becomes a perfect square
and 2 is the least number by
which you can do this

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