Question

How do you find the simplified radical form of 54?

Answer 1

Hint: In the given question, we have been asked to find the radical form of an even natural number. To solve this question, we must know the meaning of radical form. Radical form means the square root of the number. If the number is a perfect square, then it has no integer left in the square root. But if it is not a perfect square, then it has at least one integer in the square root.

Complete step-by-step answer:
The given number whose radical form is to be found is \[54\].
Radical form of a number means its square root.
So, we have to find the simplified form of \[\sqrt {54} \].
First, we find the prime factorization of \[54\] and club the pair(s) of equal integers together.
\[\begin{array}{l}2\left| \!{\underline {\,
  {54} \,}} \right. \\3\left| \!{\underline {\,
  {27} \,}} \right. \\3\left| \!{\underline {\,
  9 \,}} \right. \\3\left| \!{\underline {\,
  3 \,}} \right. \\{\rm{ }}\left| \!{\underline {\,
  1 \,}} \right. \end{array}\]
Hence, \[54 = 2 \times 3 \times 3 \times 3 = 6 \times {3^2}\]
Hence, \[\sqrt {54} = \sqrt {6 \times {{\left( 3 \right)}^2}} = 3\sqrt 6 \]
Thus, the simplified radical form of \[54\] is \[3\sqrt 6 \].

Note: When we are calculating such questions, we find the prime factorization, club the pairs together, take them out as a single number and solve for it. This requires no further action or steps to evaluate the answer.