Answer:
See below.
Step-by-step explanation:
So we want to prove that:
[tex]\sqrt8+\sqrt2=3\cdot 2^{\frac{1}{2}}[/tex]
First, simplify √8. This is the same as:
[tex]\sqrt8=\sqrt{4\cdot 2}=\sqrt4\cdot\sqrt2=2\sqrt2[/tex]
Therefore, our equation is now:
[tex]2\sqrt2+\sqrt2=3\cdot2^{\frac{1}{2}}[/tex]
Combine like terms on the left:
[tex]3\sqrt2=3\cdot 2^\frac{1}{2}}[/tex]
The square root of something is the same as taking that number to the one-half power. Thus:
[tex]3(2)^\frac{1}{2}}=3\cdot 2^\frac{1}{2}}[/tex]
Rewrite:
[tex]3\cdot2^\frac{1}{2}}\stackrel{\checkmark}{=}3\cdot2^\frac{1}{2}}[/tex]
And we're done!
