Question

Solve to get the square root of 1764 by prime factorization.

Answer 1

Hint: Prime factorization is a method of reducing the given number by dividing it successively by prime factors. To find the square root, we group the prime factors in pairs and then take individual factors out of the pair and multiply them.

Complete step-by-step solution -
We can factorize 1764 as-
$\begin{align}
  &2\left| {\underline {1764} } \right. \\
  &2\left| {\underline {882} } \right. \\
  &3\left| {\underline {441} } \right. \\
  &3\left| {\underline {147} } \right. \\
  &7\left| {\underline {49} } \right. \\
  &7\left| {\underline 7 } \right. \\
  &\;\;\left| 1 \right. \\
\end{align}$
So the given number can be written as-
$1764 = \underline {2 \times 2} \times \underline {3 \times 3} \times \underline {7 \times 7} $
So, the square root for 1764 is-
$2 \times 3 \times 7 = 42$
This is the required answer.

Note: We should note that during the factorization, we should only factorize using the prime factors. Even if we do not use prime factors, the factorization will be correct, but the pairing of factors will be wrong, hence the square root calculated will also come out to be incorrect.