Question

For the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained: $1620$

Answer 1

Step 1: Find prime factors of the given number

By the method of prime factorization, the factors of $1620$ can be determined as follows,

So, $1620=2\times 2\times 3\times 3\times 3\times 3\times 5$

$\Rightarrow 1620=\overline{2\times 2}\times \overline{3\times 3}\times \overline{3\times 3}\times 5$

Here, it can be observed that the prime factors $2$ and $3$ form pairs, while $5$ does not form a pair.

Step 2: Determine the perfect square number and its square root

Since $5$ could not form a pair.

Therefore, by dividing $1620$ by $5$, a perfect square number can be obtained.

So, the perfect square number $=\frac{1620}{5}=324$

Now, the square root of the above perfect square number is,

$\sqrt{324}=\sqrt{2\times 2\times 3\times 3\times 3\times 3}$

$\Rightarrow \sqrt{324}=\sqrt{\overline{2\times 2}\times \overline{3\times 3}\times \overline{3\times 3}}$

$\Rightarrow \sqrt{324}=2\times 3\times 3$

$\Rightarrow \sqrt{324}=18$

Hence, the smallest whole number by which $1620$ should be divided to get a perfect square is $5$ and the required perfect square number and its square root are $324$ and $18$ respectively.