Question

What is the simplest radical form of 24?

Answer 1

Hint: The given question asks us to find the simplest radical form of the number 24. Simplest radical form means that we have to express the given radical in the simplest way possible such that there are no more square roots, cube roots, fourth roots, … , \[{{n}^{th}}\] root. We will first write the factors of 24, then according to the frequency of a similar factor occurring, we will find the square root or the cube root or so on. Then, we will reduce it to the simplest possible form and we will have the simplest radical form of the given number.

Complete step by step answer:
According to the given question, we are given a number 24 ad we have to find the simplest radical form of the number.
Simplest radical form here means that we have to express the given radical in the simplest form possible such that there are no more square roots, cube roots or any roots possible. We will begin our solution by first finding the factors of the given number.
The given number is 24,
The factors of 24 are,
\[24=2\times 2\times 2\times 3\]
Now, we have selected which root we have to find, we will go with the square root.
So, \[\sqrt{24}\] will be,
\[\Rightarrow \sqrt{24}=\sqrt{2\times 2\times 2\times 3}\]
On solving further, we get,
\[\Rightarrow \sqrt{24}=2\sqrt{2\times 3}\]
So, we have,
\[\Rightarrow \sqrt{24}=2\sqrt{6}\]
As we see the obtained answer cannot be reduced further,

Therefore, the simplest radical form of 24 is \[2\sqrt{6}\].

Note: The question should be understood well before attempting to write the solution. And the simplest radical does not mean that we have to carry out squares only, but we can carry out other roots like cube roots also depending upon the frequency of the factors occurring.