Question

Simplify: 8x11−−√−10x11−−√
(1 point)
Responses

18x22−−√
18 x square root of 22

−2x
negative 2 x

−2x22−−√
negative 2 x square root of 22

−2x11−−√

Answer 1

To simplify the expression \( \sqrt{8}x - \sqrt{10}x \):

1. Factor out \( x \):
\[
x(\sqrt{8} - \sqrt{10})
\]

2. Simplify \( \sqrt{8} \):
\[
\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}
\]

So the expression becomes:
\[
x(2\sqrt{2} - \sqrt{10})
\]

Since \( \sqrt{10} \) cannot be simplified further and cannot combine with \( 2\sqrt{2} \), this expression is as simplified as it can get.

Now let's evaluate options provided:

- \( 18\sqrt{22} \) (not correct)
- \( -2x \) (not correct)
- \( -2x\sqrt{22} \) (not correct)
- \( -2x\sqrt{11} \) (not correct)

It appears that none of the provided responses match the simplified expression. Therefore, the correct answer based on simplification is:

\[
x(2\sqrt{2} - \sqrt{10})
\]

Make sure to double-check the original expression or options provided. Would you like to clarify or provide the expression again?