Question

question
express in simplest radical form given ( x > 0 ).
( -2sqrt{27x^5} - x^2sqrt{3x} )
answer attempt 1 out of 2

Explanation:

Step1: Simplify $\sqrt{27x^5}$

Break down radicand into factors:
$\sqrt{27x^5} = \sqrt{9 \cdot 3 \cdot x^4 \cdot x} = \sqrt{9x^4} \cdot \sqrt{3x} = 3x^2\sqrt{3x}$

Step2: Substitute back into original expression

Replace $\sqrt{27x^5}$ with simplified form:
$-2 \cdot 3x^2\sqrt{3x} - x^2\sqrt{3x} = -6x^2\sqrt{3x} - x^2\sqrt{3x}$

Step3: Combine like terms

Add the coefficients of like radical terms:
$-6x^2\sqrt{3x} - x^2\sqrt{3x} = (-6 - 1)x^2\sqrt{3x} = -7x^2\sqrt{3x}$

Answer:

$-7x^2\sqrt{3x}$