Question

Find the smallest whole number by which 2645 should be multiplied so as to get a perfect square. Also find it square root.

Answer 1

Hint: In the prime factorization of a number if the number does not contain a pair of prime factors then it is not a perfect square.

Complete step by step answer:
 First do the prime factorisation of the number 2645

Therefore,
\[2645=5\times 23\times 23\]
Since, in the above prime factor 5 is a single prime number.
Therefore, 5 must be multiplied with the given number to convert it into a perfect square.
Hence,
\[\begin{align}
  & 2645\times 5=5\times 5\times 23\times 23 \\
 & 13225=5\times 5\times 23\times 23 \\
\end{align}\]
Now, find the perfect square
To find the perfect square of the number take a pair of numbers as a one prime number out of the square root and then multiply.
\[\sqrt{13225}=\sqrt{5\times 5\times 23\times 23}\]
Take pair of prime number out of square root and multiply
\[\begin{align}
  & \sqrt{13225}=5\times 23 \\
 & \sqrt{13225}=115 \\
\end{align}\]

Therefore, the square root is 115.

Note: To find the square root of any number always take out the pair of prime numbers out of the square root and then multiply.