Question

How do you evaluate 3√8 + 4√50?

Answer 1

• 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 `26sqrt(2)`

Explanation:

Let's factorize the numbers inside the square roots.
`3 sqrt(8) + 4 sqrt(50)`
`3 sqrt(2*2*2) + 4sqrt(2*5*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(ab) = sqrt(a) * 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 * 2) * sqrt(2) + 4sqrt(5 * 5) * sqrt(2)`
`3 sqrt(4) * sqrt(2) + 4sqrt(25) * sqrt(2)`

We already know that `sqrt(4) = 2` and `sqrt(25) = 5`, so let's simplify what we have.

`3 * 2 sqrt(2) + 4 * 5 sqrt(2)`
`6 sqrt(2) + 20sqrt(2)`
`26 sqrt(2)`

I hope this helped :-)