Question

istribute and simplify these radicals.

Answer 1

I don’t see the specific expressions — can you paste them? Meanwhile here are the rules and quick examples so you can apply them to your problems.

Rules
- You can distribute multiplication over addition: a(√b + √c) = a√b + a√c. If a is a radical use √x·√y = √(xy).
- Simplify each radical by factoring out perfect powers (for square roots, pull out perfect squares): √(n·k^2) = k√n.
- Combine like terms only when the radicands match (e.g., 4√3 + 3√3 = 7√3).
- You cannot distribute a square root over addition: √(a + b) ≠ √a + √b.
- If required, rationalize denominators: multiply numerator and denominator by a conjugate or appropriate radical.

Examples
1) 2(√12 + √18)
- Distribute: 2√12 + 2√18
- Simplify: √12 = 2√3, √18 = 3√2
- Result: 2·2√3 + 2·3√2 = 4√3 + 6√2

2) √3(√5 + √12)
- Multiply: √15 + √36
- Simplify: √36 = 6
- Result: √15 + 6

3) (√8 + √2)√3
- Distribute: √24 + √6
- Simplify: √24 = 2√6
- Combine: 2√6 + √6 = 3√6

4) Rationalize: 3/√5
- Multiply by √5/√5 → 3√5/5

Note on incorrect distribution:
- √(9 + 16) = √25 = 5, but √9 + √16 = 3 + 4 = 7 (not equal).

Send the specific radicals you need distributed and simplified and I’ll work them out step by step.