Question

What is $ \sqrt {119} $ in simplest radical form?

Answer 1

Hint: The word radical in the given question means the number should have some type of root in it , it can be a square root or it can be a cube root or even higher roots, for example $ \sqrt 2 $ is a radical . The number given in the question has to be solved down to its simplest form possible in terms of a radical. The simplest form for the given number (or radical) will be found out by finding out if any one of the factors of $ 119 $ is a perfect square the number will come out of the root sign and the remaining number will be the radical form. If the number does not have any perfect squares as its factor we can say the number is already in its simplest radical form

Complete step by step solution:
The simplest form for the given number will be found out by finding out if any one of the factors of $ 119 $ is a perfect square the number will come out of the root sign and the remaining number will be the radical form
We now factorize $ 119 $
The number $ 119 $ on factorization gives
 $ 119 = 17 \times 7 $
Since no factor is perfect square we can say that the number
 $ \sqrt {119} $ Is already in its simplest radical form.

Note: If a number which is radical does not have any factors that are perfect square that means that the number is already in its simplest radical form. For example $ \sqrt 2 $ is already in its simplest radical form as none of its factors are perfect squares.