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). )

3√2x + x√8x - 5√18x

3√2x + 2x√2x - 15√2x

I think there are some typos involving a missing "x"

However, if you meant

3x√2x + x√8x - 5x√18x

then you get

3x√2x + 2x√2x - 15x√2x = -10x√2x
so I don't see the error.

Part 1: Nakim made an error while simplifying the given expression. Instead of getting -10x times the square root of 2x as the answer, the correct simplified expression is -3sqrt(2x) + sqrt(8x) - 5sqrt(18x).

Part 2: To simplify the expression, we need to apply the distributive property and combine like terms. Let's break it down step by step:

Given expression: 3sqrt(2x) + x(sqrt(8x)) - 5(sqrt(18x))

Step 1: Simplify the square roots within the expression.
- sqrt(2x) cannot be simplified further.
- sqrt(8x) can be simplified as 2sqrt(2x) because 8 can be factored into 4 * 2.

The expression becomes: 3sqrt(2x) + x(2sqrt(2x)) - 5(sqrt(18x))

Step 2: Simplify the coefficients and combine like terms.
Here, we will distribute "x" to get 2x times sqrt(2x). Also, remember that we have -5 multiplying sqrt(18x).

The expression becomes: 3sqrt(2x) + 2x(sqrt(2x)) - 5sqrt(18x)

Step 3: Simplify the square roots further if possible.
- sqrt(2x) cannot be simplified further.
- sqrt(18x) can be simplified as 3sqrt(2x) because 18 can be factored into 9 * 2.

The final simplified expression is: 3sqrt(2x) + 2x(sqrt(2x)) - 5(3sqrt(2x))
Simplified further: 3sqrt(2x) + 2x(sqrt(2x)) - 15sqrt(2x)

So, the correct simplified expression is -3sqrt(2x) + sqrt(8x) - 5sqrt(18x).