Math

QuestionSimplify: 15x65x53x3\frac{\sqrt{15 x^{6}}}{\sqrt{5 x^{5}}} \cdot \sqrt{3 x^{3}}. What is the final result?

Studdy Solution

STEP 1

Assumptions1. We are given the expression 15x65x53x3\frac{\sqrt{15 x^{6}}}{\sqrt{5 x^{5}}} \cdot \sqrt{3 x^{3}}. . We need to perform the operations and simplify this expression.

STEP 2

First, let's simplify the fraction by dividing the numerator and the denominator by their common factor.
15x65x5=15x65x5\frac{\sqrt{15 x^{6}}}{\sqrt{5 x^{5}}} = \sqrt{\frac{15 x^{6}}{5 x^{5}}}

STEP 3

Now, simplify the fraction inside the square root.
15x65x5=3x\sqrt{\frac{15 x^{6}}{5 x^{5}}} = \sqrt{3 x}

STEP 4

Next, multiply the simplified fraction with the remaining part of the expression.
3x3x3=9x4\sqrt{3 x} \cdot \sqrt{3 x^{3}} = \sqrt{9 x^{4}}

STEP 5

Finally, simplify the square root.
9x4=3x2\sqrt{9 x^{4}} =3 x^{2}So, the simplified form of the given expression is 3x23 x^{2}.

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