# How do you evaluate 3√8 + 4√50?

Nov 8, 2015
• Check for factors that are quadratic numbers inside the roots
• Try to make the square roots the same, i.e. $\sqrt{3}$ or $\sqrt{2}$
• Add them together if the square roots have the same value
The answer will be $26 \sqrt{2}$

#### Explanation:

Let's factorize the numbers inside the square roots.
$3 \sqrt{8} + 4 \sqrt{50}$
$3 \sqrt{2 \cdot 2 \cdot 2} + 4 \sqrt{2 \cdot 5 \cdot 5}$

We can see that we have common factors, let's isolate them!
Working with square roots, we can separate factors in the same square root:
$\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$
Let's do this with our common factors.
(NOTE: We only want TWO common factors as long as we have a square root).

$3 \sqrt{2 \cdot 2} \cdot \sqrt{2} + 4 \sqrt{5 \cdot 5} \cdot \sqrt{2}$
$3 \sqrt{4} \cdot \sqrt{2} + 4 \sqrt{25} \cdot \sqrt{2}$

We already know that $\sqrt{4} = 2$ and $\sqrt{25} = 5$, so let's simplify what we have.

$3 \cdot 2 \sqrt{2} + 4 \cdot 5 \sqrt{2}$
$6 \sqrt{2} + 20 \sqrt{2}$
$26 \sqrt{2}$

I hope this helped :-)