Question

How do you simplify sqrt(8x)?

I know that to simplify something like sqrt(8x^2), the simplified version would be:

x * sqrt(8)

But how can I simplify the expression if the 8x under the radical isn't squared?

Answer 1

To simplify √(8x), factor 8 into (2²)× 2, then take the square root of 2² which is 2, and multiply it by √(2x), yielding the simplified form of 2√(2x).

Step-by-step explanation:

To simplify the square root of 8x, which is √(8x), we need to break down the number 8 into its prime factors. Since 8 is 2 cubed (2³), which can also be written as 2× 2× 2, we pull out pairs of factors from under the square root sign.

To show this step by step:

1. First, express 8 as 4× 2, which is the same as (2²)× 2.
2. Since the square root of 2² is 2, √(8x) can be rewritten as √((2²)× 2x) = √(2²) √(2x).
3. This simplifies to 2√(2x).

So, the simplified form of √(8x) is 2√(2x).

Answer 2

The answer is
`2√(2x)`

You're right about the x in the root not being able to simplify, but that just means that the x stays inside the square root. The 8 on the other hand simplifies to:

`√(4*2) =2 √(2)`

So this means that
`√(8x) = 2√(2x)`