Question

Distribute and simplify these radicals.

Answer 1

I don’t see the expressions you want distributed — could you paste them?

Meanwhile, here’s a quick reminder of the steps and a few examples so you can check your work:

General steps
- If you’re distributing a factor into a sum/difference of radicals, first simplify each radical (factor out perfect squares).
- Combine like radicals (same radicand) before or after multiplying the outside factor.
- When multiplying two radicals, use √a·√b = √(ab) (valid for nonnegative a,b).
- Note: √(a + b) ≠ √a + √b, so you cannot “distribute” across addition inside a single radical.

Examples

1) 3(√18 + √8)
- √18 = 3√2, √8 = 2√2
- 3(3√2 + 2√2) = 3(5√2) = 15√2

2) −2(√50 − √8)
- √50 = 5√2, √8 = 2√2
- −2(5√2 − 2√2) = −2(3√2) = −6√2

3) (1/2)(√45 + 3√5)
- √45 = 3√5
- (1/2)(3√5 + 3√5) = (1/2)(6√5) = 3√5

4) √3(√12 + √48) — multiply radicals directly
- √3·√12 = √36 = 6, √3·√48 = √144 = 12
- Sum = 6 + 12 = 18

If you paste the specific radicals you need distributed and simplified, I’ll do them step by step.