QuestionSimplify the expression $-4x^2\sqrt{3x^3} + 7x^3\sqrt{12x}$ into simplest radical form.

Studdy Solution

STEP 1

Assumptions1. The expression to simplify is -4x^\sqrt{3x^3} +7x^3\sqrt{12x} . The operations are multiplication, addition, and square root3. We are to express the simplified expression in simplest radical form

STEP 2

We start by simplifying each term individually. Let's start with the first term -4x^2\sqrt{x^}.
We can rewrite x^ under the square root as $x^2 \cdot x$ and then take $x^2$ out of the square root because the square root of $x^2$ is $x$ .
-4x^2\sqrt{x^} = -4x^2\sqrt{x^2 \cdot x} = -4x^2 \cdot x\sqrt{x} = -4x^\sqrt{x}

STEP 3

Now we simplify the second term $7x^3\sqrt{12x}$ .
We can rewrite $12x$ under the square root as $\cdot3x$ and then take $out of the square root because the square root of$ is $2$ .
$7x^3\sqrt{12x} =7x^3\sqrt{ \cdot3x} =7x^3 \cdot2\sqrt{3x} =14x^3\sqrt{3x}$

STEP 4

Now we substitute the simplified terms back into the expression.
$-4x^2\sqrt{3x^3} +7x^3\sqrt{12x} = -4x^3\sqrt{3x} +14x^3\sqrt{3x}$

STEP 5

Since both terms are like terms (they both have $x^3\sqrt{3x}$ ), we can combine them.
$-4x^3\sqrt{3x} +14x^3\sqrt{3x} = (-4 +14)x^3\sqrt{3x} =10x^3\sqrt{3x}$ The simplified expression in simplest radical form is $10x^3\sqrt{3x}$ .

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