Question

Find the smallest number by which 7776 is to be multiplied to get a perfect square.

Answer 1

Given, a number as $7776$. We need to find out a number which if divided by the given number we should get a perfect square.

Step:$1$ Resolve $7776$ into prime factors

$7776=2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3$

Step:$2$ By pairing the factors obtained

$\Rightarrow 7776=(2\times 2)\times (2\times 2)\times (3\times 3)\times (3\times 3)\times 2\times 3$

Step:$3$ Dividng the number woth the factor which are alone.

Here,$2,3$ are in pairs and $3,2$ are alone.

$\Rightarrow 3\times 2=6$

$\Rightarrow \frac{7776}{6}=1296$

Hence, $6$ is the smallest number which is to be multiplied to the given number to get perfect square.