Question

How do you find the simplest radical form of \[32\ ]?

Answer 1

Hint: In the above question we are given a number that is \[32\] which is a real number and we are asked to write its radical form. So while approaching such kind of questions one should know about the radical form and the real numbers as the radical expression or the forms are those expressions which contain the square root, cube root, or fractional form in their expressions and the real numbers are those numbers which we normally use they can be negative or the positive whole or decimal. In this question, the real number is given which we would break into its smallest factors then find the radical expression.

Complete step-by-step answer:
Here we are given a term that is \[32\] and we are asked the method to simplify it into the radical form.
So firstly by seeing the number we can say that is a real number (the numbers that we use in real life) and we are asked to convert it into the radical expression (the expressions which contain the square root, cube root, or fractional form in their expressions) and it would be done by breaking the number into its factors then taking a square root of it So the simplification of the given term \[32\] into the radical form is done as-
We are given a term that is \[32\] we would first take a square root of it that is –
=\[\sqrt {32} \]
Now we would split the number into the simplest factors that are-
=\[\sqrt {2{\times}2{\times}2{\times}2{\times}2} \]
Now we would take out the perfect square and that comes out to be as-
=\[4\sqrt 2 \]
So the radical answer form is \[4\sqrt 2 \] which shows it’s a non-perfect square too (the real numbers whose square root are a real number)

Note: While solving this kind of question one should know about the radical expression and the method to convert the numbers to the radical expression. Also, the utter concentration should be taken while getting the square for the number which would lead to precision in the solution and getting the right answer also.