Question

}{\sqrt{8} }" alt="\frac{\sqrt{3} }{\sqrt{8} }" align="absmiddle" class="latex-formula">

Answer 1

Answer:

Step-by-step explanation:

√8/√3

√8≈2.83

√3≈1.73

Therefore your answer should be ABOUT

2.83/1.73

Simplify to about 1.64

Answer 2

Explanation:

This is a radical (it contains square roots). A known rule of algebraic expressions is that you can NEVER have a square root in the denominator. Therefore, we must go through a process called rationalization. This process is shown below:

$\frac{2\sqrt{2} }{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} }$  

First, you want to simplify the radical $\sqrt{8}$. This is quite easy. Firstly, divide the square root by the smallest prime number that you can. This is 2 (dividing by 1 is pointless). This gives us $\frac{\sqrt{8} }{2}$. Dividing this will give us $\sqrt{2}$. This is because we have to split up the radical on top first to give us $2\sqrt{2}$. Then, dividing by 2 leaves us with an isolated $\sqrt{2}$.

Then, we multiply by the radical in the denominator in order to eliminate the radical in the denominator (it sounds odd, but I will demonstrate it so it makes sense). This gives us $\frac{2\sqrt{2} }{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} }$.

This next step is doing simple multiplication. We always do cross-multiplication in this step because it is easier to demonstrate. Therefore, we are going to have a little bit of simplifying to do (don't worry, I have worked this all out for you).

$2\sqrt{2} *\sqrt{3}$ = $2*(\sqrt{2}*\sqrt{3} )$

$\sqrt{2} * \sqrt{3} = \sqrt{2*3}$

$\sqrt{2*3} = \sqrt{6}$    (Now, reintroduce the coefficient of 2)

⇒ $2\sqrt{6}$

The denominators cancel out and simply become $3$ (multiplying one square root by another is the same operation as multiplying the two numbers together and then taking the square root of them). This leaves us with $\frac{2\sqrt{6} }{3}$.

Then, we can either simplify this answer into a decimal or we can leave it as is (this is our final answer). Simply use a calculator and simplify the result if you need to in order to get $\frac{2\sqrt{6} }{3} = 1.63299$.