The sum of cubes of first five consecutive numbers starting from one is a perfect square of a number, then the number is .

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Solution

The correct option is A 15
We can observe the pattern accordingly:
$1^{3}$ + $2^{3}$ = 9 = $3^{2}$
$1^{3}$ + $2^{3}$ + $3^{3}$ = 36 = $6^{2}$
$1^{3}$ + $2^{3}$ + $3^{3}$ + $4^{3}$ = 100 = $10^{2}$
$1^{3}$ + $2^{3}$ + $3^{3}$ + $4^{3}$ + $5^{3}$ = 225 = $15^{2}$

For the first five consecutive number we get $15^{2} .$
Hence, the number is 15.

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