Question

Simplify: 9√5x - √5x
A.)10√5x
B.)8√5x
C.) √5x
D.)7

Answer 1

the answer is b because 1 rad5x is subtracted from 9 rad5x

Answer 2

`8√(5x)`

Explanation:

I'm assuming the "x" is also under the square root, making the equation:

`9√(5x) - √(5x)`

This may look difficult to simplify at first, but this is really a matter of subtracting coefficients. It may help to explicitly write the coefficient of the square root, which is one.

`9√(5x) - 1√(5x)`

This can be thought of as having 9 of something, and taking away 1 of that thing, this logically means you have 8 left. In this case, that "thing" is the:
`√(5x)`, so we have 8 of this, or in other words:
`8√(5x)` which is our answer! Note: It also may help to think of the equation as:
`9x-x` which you may be more used to, making it easier to remember just to subtract coefficients, except in this case,
`x=√(5x)`

Another way to think of this problem, which will lead to the same step of subtracting one from nine, is factoring. Starting with the equation:

`9√(5x) - 1√(5x)`

We can factor out the
`√(5x)` which leads to the equation:

`√(5x)(9-1)`

now just simplify that 9-1, and you get:

`8√(5x)`