Asked by kelvin calin
Rewrite this radicand as two factors, one of which is a perfect square.
All Answers 1
Answered by
GPT-5 mini
AI
I don't see the radicand you want changed — could you paste it?
Meanwhile, here's a quick method you can use and some examples.
Method
1. Factor the radicand into primes and variable powers.
2. Group each prime/variable exponent into pairs (for a square). Any paired factors make up the perfect square; unpaired ones form the other factor.
3. Write radicand = (perfect square) × (remaining factor).
Examples
- 72 = 2^3·3^2 → perfect square = 2^2·3^2 = 36, remaining = 2 → 72 = 36·2.
- 50 = 2·5^2 → 50 = 25·2.
- 18 = 2·3^2 → 18 = 9·2.
- 48 = 2^4·3 → 48 = 16·3.
- 72x^3y^4 = (2^3·3^2)·x^3·y^4 → pair exponents: perfect square = 36·x^2·y^4, remaining = 2x → 72x^3y^4 = 36x^2y^4 · 2x.
If you give your specific radicand I’ll rewrite it for you.
Meanwhile, here's a quick method you can use and some examples.
Method
1. Factor the radicand into primes and variable powers.
2. Group each prime/variable exponent into pairs (for a square). Any paired factors make up the perfect square; unpaired ones form the other factor.
3. Write radicand = (perfect square) × (remaining factor).
Examples
- 72 = 2^3·3^2 → perfect square = 2^2·3^2 = 36, remaining = 2 → 72 = 36·2.
- 50 = 2·5^2 → 50 = 25·2.
- 18 = 2·3^2 → 18 = 9·2.
- 48 = 2^4·3 → 48 = 16·3.
- 72x^3y^4 = (2^3·3^2)·x^3·y^4 → pair exponents: perfect square = 36·x^2·y^4, remaining = 2x → 72x^3y^4 = 36x^2y^4 · 2x.
If you give your specific radicand I’ll rewrite it for you.
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