Question

How do you find the simplest radical form of $98$?

Answer 1

Hint: In this question we have to write the number$98$in simplest radical form. To write we are required to know the definition of the simplest radical form, know the square root of numbers or method to find the square root of a number. To find the simplest radical form of a number we will remove all square root, cube roots and so on.

Complete step-by-step solution:
Let us try to solve this question in which we need to find the simplest radical form of number $98$. Before solving this we see the definition of simplest radical form by simplest radical form we mean there are no more square roots, cube roots and higher order roots in the radical. To solve this we also know about square root, cube root etc.

Here we need to find the simplest radical form of $98$. In number $98$ have a square of number$7$. We have to remove this square from $98$ to write it in the simplest radical form. We will first write the prime factor of number 98. In prime factor we write numbers only using prime divisors product.

So the prime factor of $98 = 2 \times 7 \times 7$. Now taking square of the number we get
$\sqrt {98} = \sqrt {2 \times 7 \times 7} $
Now $7$will come out of square root and we get,
$\sqrt {98} = 7\sqrt 2 $

Hence 98 in the simplest radical form is$7\sqrt 2 $.

Note: In mathematics we have a theorem related to prime factors called Fundamental theorem of Arithmetic which says that any natural number greater than \[1\]can be written as a product of primes and the prime factorization is unique.