Question

What is the square root of 5 divided by the square root of 8?

Answer 1

Hint: We firstly explain the concept of square roots. Then we shall divide the two square roots. The denominator term is $\sqrt{8}$ which is irrational, we convert this to a rational form by multiplying both the numerator and denominator by $\sqrt{8}.$ Then, we need to simplify the equation cancelling the common factors and representing the division of the two terms in its simplest form.

Complete step-by-step solution:
To solve this question, we consider the statement given in the question. This translates to an equation form given by,
$\Rightarrow \dfrac{\sqrt{5}}{\sqrt{8}}$
This has the denominator as an irrational term. We need to rationalize this. In order to do so, we multiply both the numerator and denominator by the denominator term $\sqrt{8}.$
$\Rightarrow \dfrac{\sqrt{5}\times \sqrt{8}}{\sqrt{8}\times \sqrt{8}}$
We know the product of two same root terms is the same as the term without the root.
$\Rightarrow \dfrac{\sqrt{5}\times \sqrt{8}}{8}$
We also multiply both the terms in the numerator and represent them as,
$\Rightarrow \dfrac{\sqrt{40}}{8}$
The numerator can be split as a product of two terms 4 and 10.
$\Rightarrow \dfrac{\sqrt{4\times 10}}{8}$
The term 4 can be written as ${{2}^{2}},$ and this term comes outside the square root as just 2.
$\Rightarrow \dfrac{\sqrt{{{2}^{2}}\times 10}}{8}=\dfrac{2\sqrt{10}}{8}$
Cancelling the two terms in the numerator and denominator having a common factor of 2,
$\Rightarrow \dfrac{\sqrt{10}}{4}$
Now this is the answer in terms of fractions. We can further simplify this by taking the square root value of 10 which is given as $\sqrt{10}=3.1623.$ Substituting this in the above equation,
$\Rightarrow \dfrac{3.1623}{4}$
Dividing the two terms using the decimal division concept,
$\Rightarrow \dfrac{3.1623}{4}=0.7906$
Hence, the value of the square root of 5 divided by the square root of 8 is $\dfrac{\sqrt{10}}{4}$ or $0.7906.$

Note: It is important to know the concepts of square roots to solve this question. One important concept here is the rationalization of a denominator. In order to rationalize a denominator, we multiply both the numerator and denominator by the same denominator term. We can also rationalize the numerator by multiplying both the numerator and denominator by the same numerator term. We also need to know the concept of decimal division and the conversion from a square root to a decimal.