Question

How do you simplify the \[3\] square root \[125\]?

Answer 1

Hint: in the above question we are given an expression that is \[3\] square root \[125\]which is a radical expression with a cube root. So while approaching such kind of questions one should know about the radical expression and the cube root of the expression as the radical expression are the those expressions which contain the square root , cube root or fractional form in their expressions and the cube root of an expression is the number which when cubed produces the same expression.

Complete step-by-step answer:
Here we are given a term that is \[3\] square root \[125\] and we are asked to simplify it. So firstly by seeing the expression given we can say that it is a radical expression (the expressions which contain the square root, cube root or fractional form in their expressions) and it has cube root also which means we need to find that number which when cubed or multiplied with itself gives the number that is given to us and asked a cube root for it. So the simplification of the given term \[3\] square root \[125\] is done as-\[3\] Square root \[125\] means that we need to find the cube root of the number \[125\] that is –\[\sqrt[3]{{125}}\]
Breaking the above term into its further factors to get the desired answer that is as follows-
\[\sqrt[3]{{5{\times }5{\times}5}}\]
\[ = 5\]
So the cube root of the number\[125\] is \[ = 5\]
Hence the required answer for the \[3\] square root \[125\] is \[ = 5\]
Note: While solving this kind of the question one should know about the cube root of the numbers and their symbolic representation and the utter concentration which would lead to the precision in the solution and getting the right answer also