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

\( 3 \sqrt{2x} + x \sqrt{8x} - 5 \sqrt{18x} \)
\( = 3 \sqrt{2x} + x \sqrt{4 \times 2x} - 5 \sqrt{9 \times 2x} \)
\(= 3 \sqrt{2x} + 2x \sqrt{2x} - 5 \times 3\sqrt{2x} \)
\(= 3 \sqrt{2x} + 2x \sqrt{2x} - 15 \sqrt{2x} \)
\(= (3 + 2x - 15)\sqrt{2x} \)

Answer 2

So which step would nakim have messed up on?

Answer 3

What Nakim did wrong was that he went from:
\( (3 + 2x - 15) \sqrt{2x} \)
to:
\(-10x \sqrt{2x} \)

\( (3 + 2x - 15) \sqrt{2x} \)
\(= (2x - 12) \sqrt{2x} \)

\(3 + 2x - 15 = 2x - 12 \)
\(3 + 2x - 15 \ne -10x \)

You can only combine like terms, and \(2x\) and \(-12x\) are not like terms.