Question

Help please! <3 Simplify the expression to find the correct answer. Show your work and explain how you got that answer.
`(1)/(3)√(21)-(2)/(3)√(3) x √(7)` A.
`-(1)/(3)√(21)` B.
`(2)/(3)√(21)` C.
`(2)/(3)√(18×7)` D.
`-(1)/(3)√(63)x√(7)`

Answer 1

Answer: Choice A)
`-(1)/(3)√(21)`

=====================================================

Work Shown:

I'm guessing that the x you wrote is to signify multiplication. If so, then one way to do the steps is shown in the attached image below.

In step 2, I used the rule that sqrt(x)*sqrt(y) = sqrt(x*y).

Answer 2

-1/3 sqrt(21)

Explanation:

1/3 sqrt(21) - 2/3 sqrt(3) * sqrt(7)

We know sqrt(a) * sqrt(b) = sqrt(ab)

1/3 sqrt(21) - 2/3 sqrt(21)

Factor out sqrt(21)

sqrt(21) (1/3-2/3)

sqrt(21) (-1/3)

-1/3 sqrt(21)