Question

Find the smallest number by which 35574 is to be multiplied to get a perfect square and also find the square root of the resulting number

Answer 1

Answer:

Solution :-

We have to find the smallest number by which 720

should be multiplied to get a perfect square

Here 720=2×2×2×2×3×3×5

We have pairs of 2 and 3 but there is only one 5

Now if we multiply 720 by 5 then we get three

complete pairs hence the resultant number will be

perfect square

Hence 720×5=(2×2)×(2×2)×(3×3)×(5×5)

∵

720×5

=2×2×3×5=60

Answer 2

Answer:

smallest number by which the number  is being multiplied is 6 and the square root of the required number is 462

Step-by-step explanation:

as per the data given in the question , there is a number we have to multiply it with some number to get a complete square.

the number given is 35574

we need to prime factorise it to check that how many incomplete pairs we have

$35574= 2 * 17787\\=2*3* 5929\\=2*3* 11*539\\=2*3*11*11*49\\=2*3*11*11*7*7$

when we observe the prime factorisation,

when a number is a complete square , in its prime factorisation every number is in pair

so to make it a complete square we will multiply by the number with the incomplete pair.

so, we will multiply the number 35574 by 2 and 3

and the resulting number ie. 213444

the square root of resulting number is

$\sqrt{213444}=\sqrt{2*3*2*3*11*11*7*7}$

we will take pairs out,

$\sqrt{213444}= 2*3*11*7\\= 462$

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