Question

Nakim simplified 3 times the square root of 2x plus x times the square root of 8x minus 5 times the square root of 18x and got -10x times the square root of 2x for an answer.

Part 1: Using complete sentences, explain what Nakim did wrong.

Part 2: Show all your work to simplify the expression.

(You can use "sqrt()" to show a square root. For example, 7 times the square root of a can be written as 7sqrt(a). )

Answer 1

\[3\sqrt{2x} + x \sqrt{8x} - 5 \sqrt {18x} = -10x \sqrt {2x} \]

Apparently, he rewrote it like this:

\[3\sqrt{2x} + x \sqrt{4*2x} - 5 \sqrt{9*2x}\]

\[3\sqrt{2x} + 2x \sqrt{2x} - 15\sqrt{2x}\]

and then he decided he could just add those 3 terms together, ignoring the fact that only one of them had that pesky x in front, giving him \[(3x+2x-15x)\sqrt{2x} = -10x \sqrt{2x}\]

However, the correct simplification would be

\[3\sqrt{2x} + 2x \sqrt{2x} - 15\sqrt{2x} = (3-15)\sqrt{2x} + 2x \sqrt{2x} = -12\sqrt{2x}+2\sqrt{2}x^{3/2}\]

Answer 2

Oh :o Okay, thank you so much!