Question

How do you solve `sqrt(50)+sqrt(2)` ?

Answer 1

You can simplify `sqrt(50)+sqrt(2) = 6sqrt(2)`

Explanation:

If `a, b >= 0` then `sqrt(ab) = sqrt(a)sqrt(b)` and `sqrt(a^2) = a`

So:

`sqrt(50)+sqrt(2) = sqrt(5^2*2)+sqrt(2) = sqrt(5^2)sqrt(2) + sqrt(2)`

`= 5sqrt(2)+1sqrt(2) = (5+1)sqrt(2) = 6sqrt(2)`

In general you can try to simplify `sqrt(n)` by factorising `n` to identify square factors. Then you can move the square roots of those square factors out from under the square root.

e.g. `sqrt(300) = sqrt(10^2*3) = 10sqrt(3)`