Multiply and simplify. Assume that no radicands were formed by raising negative numbers to even powers.
√6x^3 * √18x^2 =
√2 * 3 * x^3 * √2 * 3^2 * x^2 =
√2 * 3x^2x * √2 * 3^2 * x^2 =
6x^2 * √3x
Is this correct?? If not can you show me the correct steps? Please and thank you.
I assume you meant:
√(6x^3) * √(18x^2)
= √(108x^5)
= √36*√3*√x^4*√x
= 6*√3*x^2*√x
= 6√(3x)x^2
= 6x^2√(3x)
I don't know how you fudged that answer looking at your second line, which is totally wrong
it should be
√2 * √3 * √x^3 * √2 * √9 * √x^2
then
= √6 * x√x * √2 * 3 * x
= 3√12 * x^2√x
= 3*√4*√3 * x^2 * √x
= 6√(3x) x^2 or
= 6x^2 √(3x)
To multiply and simplify the expression √6x^3 * √18x^2, you can follow these steps:
1. Split the square roots: √6x^3 * √18x^2 = (√6 * √18) * (x^3 * x^2)
2. Simplify the square roots separately: √6 = √2 * √3, and √18 = √2 * √9 = √2 * 3
3. Combine the simplified square roots with the variables: (√2 * √3) * (√2 * 3) * (x^3 * x^2)
4. Multiply the numbers outside the square roots: 2 * 3 = 6
5. Multiply the variables with the same base: x^3 * x^2 = x^(3+2) = x^5
6. Combine all the results: 6 * (√2 * √3) * (x^5)
The final simplified expression is 6√6x^5. So, the given answer (6x^2 * √3x) is not correct.