Question

How do you simplify \[\sqrt{\dfrac{96}{8}}\]?

Answer 1

Hint: In this problem, we have to simplify the given square root. We can first take the numerator and we can use a multiplication table to separate it. We can write the numerator as \[12\times 8\]. We can then cancel the similar terms in the numerator and the denominator to simplify the step. We can then separate the remaining term to be simplified and get the value.

Complete step by step answer:
We know that the given square root to be simplified is,
\[\sqrt{\dfrac{96}{8}}\]
We can now first take the numerator and we can use a multiplication table to separate it. We can write the numerator as \[12\times 8\], we get
\[\Rightarrow \sqrt{\dfrac{12\times 8}{8}}\]
We can now cancel the similar terms in the numerator and the denominator to simplify the step, we get
\[\Rightarrow \sqrt{12}\]
We can now use multiplication table, to split the number to simplify it, we get
\[\Rightarrow \sqrt{{{2}^{2}}\times 3}\]
We can now separate the root terms in both the numerator and the denominator, using the multiplication of roots formula.
We know that the multiplication of roots formula is,
\[\Rightarrow \sqrt{xy}=\sqrt{x}\times \sqrt{y}\]
We can use this formula in the above step, we get
\[\Rightarrow \sqrt{{{2}^{2}}}\times \sqrt{3}\]
Now we can cancel the square and the square root for the first root, we get
\[\Rightarrow 2\sqrt{3}\]
Therefore, the simplified form of \[\sqrt{\dfrac{96}{8}}\] is \[2\sqrt{3}\].

Note:
We should know how to separate the number using a multiplication table in order to cancel the similar terms in an easier way. We should also remember that we can cancel the square and the square root to get the simplified form. We should know that the multiplication of terms inside the root is equal to multiplication of roots with its individual terms.