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.
Correct!
To multiply and simplify √6x^3 * √18x^2, we can apply the product rule of radicals, which states that √a * √b = √(a * b).
Step 1: Simplify the radicands.
√6x^3 can be simplified further by separating the factors under the radical:
√(2 * 3 * x^2 * x) = √2 * √3x * x
√18x^2 can be simplified similarly:
√(2 * 3^2 * x^2) = √2 * 3 * √x^2 = 3x * √2
Step 2: Multiply the simplified expressions.
(√2 * √3x * x)(3x * √2) = (√2 * 3x * √3x)(3x * √2)
Step 3: Multiply the coefficients together, and simplify the variables.
(√2 * 3x * √3x)(3x * √2) = 6x^2 * (√3x * √2)
Therefore, the correct simplification is 6x^2 * √3x.