QuestionSimplify $6x^{2}\sqrt{80x}+x\sqrt{45x^{3}}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $6x^{}\sqrt{80x}+x\sqrt{45x^{3}}$ . . We can use the properties of exponents and roots to simplify this expression.

STEP 2

First, we can rewrite the square roots as fractional exponents. $6x^{2}(80x)^{1/2}+x(45x^{})^{1/2}$

STEP 3

Next, we can simplify the terms inside the parentheses by multiplying the exponents by the fraction.
$6x^{2}(80x^{1/2})+x(45x^{3/2})$

STEP 4

Now, we can simplify the expression by multiplying the exponents.
$6x^{2+1/2}80^{1/2}+x^{1+3/2}45^{1/2}$

STEP 5

implify the exponents.
$x^{5/2}80^{1/2}+x^{5/2}45^{1/2}$

STEP 6

Now, we can simplify the square roots of the numbers.
$6x^{5/2}\cdot4\sqrt{5}+x^{5/2}\cdot3\sqrt{5}$

STEP 7

Multiply the coefficients.
$24x^{5/2}\sqrt{5}+3x^{5/2}\sqrt{5}$

STEP 8

Finally, we can combine the like terms.
$27x^{5/2}\sqrt{5}$ So, the simplified expression is $27x^{5/2}\sqrt{5}$ .

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