Question

What is the simplest radical form for $\sqrt {135} $?

Answer 1

Hint: The greatest perfect square factor method uses the greatest perfect square factor of given number to simplify to square root of the given number. The symbol $\sqrt {} $ is called the radical sign. To simplify the square root of the given number means to get the simplest radical form of the number.

Complete step-by-step solution:
The given number is $\sqrt {135} $.
First we have to find the factors of the given number.
List out the factors of the number $135$
One, three, $5,9,15,27,45,135$ find the perfect squares from the list out of the factors above.
There are two perfect squares.
They are one and nine.
At the next step divide the given number $135$ by the largest perfect square.
We find in the above step , the largest perfect square is nine
New, divide the given number by the largest perfect square, we have,
$ = \dfrac{{135}}{9}$
The multiplication of nine and fifteen is equal to $135$
That is $9 \times 15 = 135$
Therefore, after division we get,
$\dfrac{{135}}{9} = 15$
Now calculate the square root of the largest perfect square.
Therefore the square root of nine is equal to three.
$\sqrt 9 = \sqrt {3 \times 3} $
$ = 3$
Now get the answer by putting the above steps together.
Therefore the simplest radical form of $\sqrt {135} $ is $ = 3\sqrt {15} $

Note: Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube, roots, 4th roots left to find. It also means removing any radical in the denominator of a fraction. A perfect square is a number from a given number system that can be expressed as the square of a number from the same system.