Question

what is the square root of $32$ over 4 expressed in simplest radical form?

Answer 1

Hint: The greatest perfect square factor method used to find the square root of a given number. The symbol$\sqrt {} $is called a 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:
Given in the question is square root of $32$ over $4$
It will be written as in the form square root of thirty two divided by$4$
$ = \dfrac{{\sqrt {32} }}{4}$
We can expand it as like this
$ = \dfrac{{\sqrt {16 \times 2} }}{4}$
Again expand this we have
$ = \dfrac{{\sqrt {8 \times 2 \times 2} }}{4}$
$ = \dfrac{{\sqrt {4 \times 2 \times 2} \times 2}}{4}$
We can write four as multiple of two by two,
At the next step we get,
$\dfrac{{\sqrt {32} }}{4} = \dfrac{{\sqrt{2 \times 2 \times 2 \times 2 \times 2}}}{4}$
From this equation take square root
$ = \dfrac{{2 \times 2 \times \sqrt 2 }}{4}$
$ = \dfrac{{4 \times \sqrt 2 }}{4}$
$ = \sqrt 2 $
Here we get the simplest radical form for the given question is $ = \sqrt 2 $

Note: Square root of a number is a value, which on multiplication by itself gives the original number. The positive number when multiplied by it represents the square of the number. The square root of the square of the appositive number gives the original number. A square root is a value that gives the original number when multiplied by itself. To find the square root, we can use two methods. Prime factorization and long division method. The square root is just the opposite process of squaring a number. Suppose if we square a number $n$,such as${n^2}$, then the square root of${n^2}$is equal to the original number $n$.Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots 4th removing any radicals in the denominator of a fraction.