Question

Distribute and simplify the radicals below.

Answer 1

I don’t see the specific expressions you want worked. Please paste them.

Meanwhile, here are the rules and a couple of worked examples so you can apply them.

Key rules
- You can multiply a radical through a sum: r(√A + √B) = r√A + r√B (where r is any real number).
- You can multiply two square roots: √A · √B = √(AB) for A, B ≥ 0.
- Simplify a radical by factoring out perfect-square factors: √(k·m²) = m√k (with k square‑free).
- Combine like radicals: a√c + b√c = (a + b)√c.
- Do NOT distribute inside a radical: √(A + B) ≠ √A + √B in general.

Examples

1) Distribute a numeric radical:
√6(√2 + √3)
= √6·√2 + √6·√3
= √12 + √18
= √(4·3) + √(9·2)
= 2√3 + 3√2
(reorder if you like: 3√2 + 2√3)

2) Distribute a rational number:
3(√50 + √8)
= 3√50 + 3√8
= 3√(25·2) + 3√(4·2)
= 3·5√2 + 3·2√2
= 15√2 + 6√2
= 21√2

3) Distribute when the radical multiplies an expression inside a radical is not separable:
√(2(3 + 5)) is √(16) = 4, but you cannot do √2(√3 + √5). Those are different.

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