Question

How do you simplify \[{25^{\dfrac{1}{2}}}\]?

Answer 1

Hint: In the above question we are given an expression that is \[{25^{\dfrac{1}{2}}}\] which is a radical expression with a square root. So while approaching such kind of questions one should know about the radical expression and the square root of the expression as the radical expression are those expressions which contain the square root, cube root, or fractional form in their expressions and the square root of an expression is the number which when squared or multiplied twice with itself in the simpler language produces the same expression.

Complete step-by-step answer:
Here we are given a term that is \[{25^{\dfrac{1}{2}}}\] 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 square root also which means we need to find that number which when squared or multiplied with itself twice gives the number that is given to us and asked a square root for it. So the simplification of the given term \[{25^{\dfrac{1}{2}}}\]is done as-
\[{25^{\dfrac{1}{2}}}\] Means that we need to find the square root of the number \[25\] as the number \[\dfrac{1}{2}\] in the power of \[{25^{\dfrac{1}{2}}}\] implies for the square root of the number that is –
\[\sqrt[2]{{25}}\]
Breaking the above term into its further factors to get the desired answer that is as follows-
\[\sqrt[2]{{5{\times }5}}\]
\[ = 5\]
So the cube root of the number \[25\] is \[ = 5\]

Hence the required answer for the given radical expression in the question is \[{25^{\dfrac{1}{2}}}\] is \[ = 5\]

Note: While solving this kind of question one should know about the square 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.