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.

Answer 1

Is this the equation you are describing?
\[3\sqrt{2x} + x \sqrt{8x} - 5\sqrt{18x} = -10x \sqrt{2x}\]

Answer 2

yes :)

Answer 3

The first step would be to simplify all the square roots.
For example:
\[\sqrt{90} = \sqrt{9} * \sqrt{10} = 3 \sqrt{10}\]
9 is the only perfect square factor of 90.
Does that make sense?

Answer 4

yes, it does

Answer 5

Can you do that with each of the terms in your question?

Answer 6

i don't think so... aren't they already simplified?

Answer 7

No. Factor each of coefficients under the radical to find which ones have perfect squares.
coefficient = number multiplied by the variable
radical = square root sign

Answer 8

oh okay, so simplified it would be... 3*sqrt(2x) + 2x*sqrt(2x) - 15*sqrt(2x)

Answer 9

Exactly!
Now, combine like terms.

Answer 10

sqrt(2x) * (3 + 2x - 15) which equals sqrt(2x) * (-12 + 2x)... so nakim must have combined 3 + 2x - 15 to get -10x.

Answer 11

Yes.

Answer 12

oh okay thanks, i understand it better now :)

Answer 13

Great!