Question

How do you simplify \[\dfrac{5}{{\sqrt 5 }}\]?

Answer 1

Hint:In order to solve this question first, we assume a variable equal to the given number then we have to find the value of that variable in a simplified version. Then we rationalize that number. In rationalization, we multiply and divide the denominator in the expression. Then we multiply numerators and denominators. Then we cancel a factor from numerator and denominator. And the last term remaining is the simplified version of the given number.


Complete step by step answer:
We have given a number and we have to simplify that.
Let, the given number is equal to a variable.
\[x = \dfrac{5}{{\sqrt 5 }}\]
Now for further solving we have to rationalize the denominator.
On rationalizing the number.
\[x = \dfrac{5}{{\sqrt 5 }} \times \dfrac{{\sqrt 5 }}{{\sqrt 5 }}\]
On multiplying numerator and denominator.
\[x = \dfrac{{5\sqrt 5 }}{{\sqrt {25} }}\]
Now we know that 25 is a perfect square of 5. So on taking this term out from the under-root.
\[x = \dfrac{{5\sqrt 5 }}{5}\]
On canceling 5 from numerator and denominator.
\[x = \sqrt 5 \]
If we simplify \[\dfrac{5}{{\sqrt 5 }}\] then we get \[\sqrt 5 \].

Note: This is a standard question. This type of question is frequently asked in exams. We also simplify this equation directly by canceling the common factor from numerator and denominator but that is not a correct method to solve this type of question. To solve these types of questions students must have a knowledge of types of numbers and the terms like a rational number. Students often make mistakes in the rationalization part and calculation also. These types of questions also contain mathematical operators also but the same method is applicable for those also.