Question

question
express in simplest radical form given ( x > 0 ).
( -2sqrt{28x^5} + 9xsqrt{28x^3} )
answer
attempt 1 out of 2
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Explanation:

Step1: Simplify each radical term

First, factor out perfect squares from the radicands:
$\sqrt{28x^5} = \sqrt{4 \cdot 7 \cdot x^4 \cdot x} = \sqrt{4x^4} \cdot \sqrt{7x} = 2x^2\sqrt{7x}$
$\sqrt{28x^3} = \sqrt{4 \cdot 7 \cdot x^2 \cdot x} = \sqrt{4x^2} \cdot \sqrt{7x} = 2x\sqrt{7x}$

Substitute back into the original expression:
$-2 \cdot 2x^2\sqrt{7x} + 9x \cdot 2x\sqrt{7x}$

Step2: Calculate coefficients and exponents

Simplify each term's coefficients and variables:
$-2 \cdot 2x^2\sqrt{7x} = -4x^2\sqrt{7x}$
$9x \cdot 2x\sqrt{7x} = 18x^2\sqrt{7x}$

Step3: Combine like radical terms

Add the simplified like terms together:
$-4x^2\sqrt{7x} + 18x^2\sqrt{7x} = (18-4)x^2\sqrt{7x}$

Answer:

$14x^2\sqrt{7x}$