Question

How do you simplify\[\dfrac{{12}}{{\sqrt 2 }}\]?

Answer 1

Hint: For solving the given question we would try to cancel the root term in the denominator. Also, we need to know how to find the common factor between the numerator and denominator. Also, the given question describes the arithmetic operation of addition/subtraction/multiplication/division. Also, we need to know how to multiply the two root terms.

Complete step by step answer:
In the given question we have to simplify the term given below,
\[\dfrac{{12}}{{\sqrt 2 }}\]
First, we have to eliminate the root term in the denominator. For eliminating the root term in the denominator, \[\sqrt 2 \]is multiplied with numerator and denominator.
\[\dfrac{{12}}{{\sqrt 2 }} = \dfrac{{12}}{{\sqrt 2 }} \times \dfrac{{\sqrt 2 }}{{\sqrt 2 }} = \dfrac{{12 \times \sqrt 2 }}{{\sqrt {2 \times \sqrt 2 } }}\]
When the same root terms are multiplied with each other the root will be canceled.
\[\dfrac{{12}}{{\sqrt 2 }} = \dfrac{{12\sqrt 2 }}{2}\]
Let’s find the common factor between numerator and denominator. 12 can be divided by 2 and 2 can also be divided by 2. So, the common factor is 2. Let’s divide the numerator and denominator by 2. So, we get
\[\dfrac{{12}}{{\sqrt 2 }} = 6\sqrt 2 \]
We know that the value \[\sqrt 2 \]is 1.414
So, we get
\[
  \dfrac{{12}}{{\sqrt 2 }} = 6 \times 1.414 \\
  \dfrac{{12}}{{\sqrt 2 }} = 8.4852 \\
 \]
By solving the above step we get the final answer which is equal to 8.4852.

Note:
In this type of question, we would find if the root term is present in the denominator it would be eliminated by another root term. Note that when the same root term is multiplied with each other, the root will be canceled. If we multiply or divide the numerator with one term then the denominator also multiplies or divides with the same term. We cannot multiply or divide the term only with the numerator, always it should do with both numerator and denominator.