Question

(Number 5)help plzzz

Answer 1

Answer:

See below.

Step-by-step explanation:

So we want to prove that:

$\sqrt8+\sqrt2=3\cdot 2^{\frac{1}{2}}$

First, simplify √8. This is the same as:

$\sqrt8=\sqrt{4\cdot 2}=\sqrt4\cdot\sqrt2=2\sqrt2$

Therefore, our equation is now:

$2\sqrt2+\sqrt2=3\cdot2^{\frac{1}{2}}$

Combine like terms on the left:

$3\sqrt2=3\cdot 2^\frac{1}{2}}$

The square root of something is the same as taking that number to the one-half power. Thus:

$3(2)^\frac{1}{2}}=3\cdot 2^\frac{1}{2}}$

Rewrite:

$3\cdot2^\frac{1}{2}}\stackrel{\checkmark}{=}3\cdot2^\frac{1}{2}}$

And we're done!