By what numbers should each of the following be divided to get a perfect square in each case? Also , find the number whose square is the new number. (i)16562             (ii)    3698            (iii)    5103 (iv)3174               (v)     1575

Explanation

(i)By doing factorisation of `16562` we get,
`2times7times7times13times13`.
We can see that `2` is left unpaired therefore we will divide `16562` by `2`.
`=16562div2=8281`
`8281` is a perfect square of `91`.
Hence, `2` is the number by which `16562` must be divided so that the result is a perfect square.

(ii)By doing factorisation of `3698` we get,
`2times43times43`.
We can see that `2` is left unpaired therefore we will divide `3698` by `2`.
`=3698div2=1849`
`1849` is a perfect square of `43`.
Hence, `2` is the number by which `3698` must be divided so that the result is a perfect square.

(iii)By doing factorisation of `5103` we get,
`3times3times3times3times3times3times7`.
We can see that `7` is left unpaired therefore we will divide `5103` by `7`.
`=5103div7=729`
`729` is a perfect square of `27`.
Hence, `7` is the number by which `5103` must be divided so that the result is a perfect square.

(iv)By doing factorisation of `3174` we get,
`2times3times23times2323`.
We can see that `2` and `3` are left unpaired therefore we will divide `3174` by `6`.
`=3174div6=529`
`529` is a perfect square of `23`.
Hence, `6` is the number by which `3174` must be divided so that the result is a perfect square.

(v)By doing factorisation of `1575` we get,
`3times3times5times5times7`.
We can see that `7` is left unpaired therefore we will divide `1575` by `7`.
`=1575div7=225`
`225` is a perfect square of `15`.
Hence, `7` is the number by which `1575` must be divided so that the result is a perfect square.