Question

How do you simplify `5sqrt8 + 3sqrt20 - sqrt32`?

Answer 1

To add/subtract radicals, you must have equal numbers under the radicand.

Explanation:

`5sqrt(4(2))` + `3sqrt(4(5))` - `sqrt(16(2))`

= 5(2)√2 + 3(2)√5 - 4√2

= 10√2 - 4√2 + 6√5

We can now combine like terms, which would be 10√2 and -4√2, since the number under the radical sign is equal in both numbers. However, we can do nothing with 6√5, since it is not alike to any of the other terms.

= 6√2 + 6√5

So, 6√2 + 6√5 is your answer.

Here are a couple of exercises for your practice.

1. Simplify.

a) √48 - 5√27 + √75

1. Solve for x:

√96`x^2` + √24 = √864