Question

How do you simplify \[\dfrac{{15}}{{\sqrt 3 }}\]?

Answer 1

Hint: As here,\[\sqrt 3 \] is given in the denominator in the expression so in order to simplify the expression multiply both numerator and denominator by \[\sqrt 3 \] and then by using BODMAS rule simplify the expression given in the question.
Like, \[\dfrac{3}{{\sqrt 3 }} = \dfrac{{(3 \times \sqrt {3)} }}{{(\sqrt 3 \times \sqrt 3 )}} = \sqrt 3 \]
Hence, apply the concept to simplify the given expression.

Complete step by step solution:
As per information given in the question,
As we have to simplify \[\dfrac{{15}}{{\sqrt 3 }}\]
As, here \[\sqrt 3 \] is in numerator of the expression,
So, for simplifying the expression we need to multiply both numerator and denominator of the expression by \[\sqrt 3 \]
Hence,
We will get,
     \[\dfrac{{15 \times \sqrt 3 }}{{\sqrt 3 \times \sqrt 3 }}\]
So,
We know that,
The value given in denominator \[\left( {\sqrt 3 \times \sqrt 3 } \right)\] when multiplied given \[3\].
So,
We will get,
\[ \Rightarrow \dfrac{{15\sqrt 3 }}{3}\]
Here, as we know that,
\[15\] is a multiple of \[3\].
So, dividing 15 with \[3\] we will get,
\[ \Rightarrow 5\sqrt 3 \]

When the above expression is simplified the answer will be \[5\sqrt 3 \]

Note: Always remember, \[\sqrt 3 \times \sqrt 3 = 3\].
Means, when two similar square roots are multiplied with each other gives the same number.
For simplifying the expression which contains square root in the denominator , always multiply the numerator as well as denominator of the expression with the value which is in square root.