Question

What is the simplest radical form of \[\sqrt{116}\]?

Answer 1

Hint: From the question given, we have been asked to find the simplest radical form of \[\sqrt{116}\]. Here, to solve this question we have to split the number into two products where one number must be a perfect square, take the perfect square number out and leave the remaining number under square root. Here , first we are breaking \[116\] into factors, and then taking the perfect square out.

Complete step by step answer:
Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots etc.
Simplified radical form is when a number under the radical is indivisible by a perfect square other than \[1\]
We try to split the number into the product of the factors where at least one of the numbers might be a perfect square.
Start by breaking it as you would for prime factorisation, and continue until you have perfect squares
To simplify:
\[1.\]Rewrite the expression as two radicals factoring the number out into a perfect square and a non-perfect square. In this case, \[\sqrt{116}\] can be rewritten as
\[\sqrt{116}\]=\[\sqrt{2\times 58}\]=\[\sqrt{2\times 2\times 29}\]
\[\sqrt{4\times 29}\]=\[\sqrt{4}\]\[\times \]\[\sqrt{29}\]
\[2.\]Take the square root of the perfect square.
So in this case\[\sqrt{4}\]=\[2\], so the answer can be rewritten as \[2\sqrt{29}\]

Note: Students should know the perfect squares. One should concentrate while taking the perfect square number out. We have to break the number until a perfect square number is obtained. We have to note that the perfect square that we are taking out is the largest possible square and it will help reduce to the simplest form faster.