Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 3 \sqrt{x} \times 2 \sqrt{x^{3}} = 6x^{2} \)
Solution
Calculate or simplify the expression \( 3*\sqrt(x)*2*\sqrt(x^3) \).
Simplify the expression by following steps:
- step0: Solution:
\(3\sqrt{x}\times 2\sqrt{x^{3}}\)
- step1: Use the properties of radicals:
\(3\sqrt{x\times x^{3}}\times 2\)
- step2: Multiply the terms:
\(3\sqrt{x^{4}}\times 2\)
- step3: Simplify the root:
\(3x^{2}\times 2\)
- step4: Multiply the terms:
\(6x^{2}\)
The expression \(3 \sqrt{x} \times 2 \sqrt{x^{3}}\) simplifies to \(6x^{2}\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve \( 3 \sqrt{x} \times 2 \sqrt{x^{3}} \), we can begin by multiplying the coefficients and then the terms under the square roots. First, multiply the constants: \( 3 \times 2 = 6 \). Next, we simplify the square roots: \[ \sqrt{x} \times \sqrt{x^{3}} = \sqrt{x \cdot x^{3}} = \sqrt{x^{4}} = x^{2}. \] Putting it all together, we have: \[ 3 \sqrt{x} \times 2 \sqrt{x^{3}} = 6 x^{2}. \] Therefore, the final answer is \( 6x^{2} \).
