Question

Help please! <3 Simplify the expression to find the correct answer. Show your work and explain how you got that answer. src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Csqrt%7B21%7D-%5Cfrac%7B2%7D%7B3%7D%5Csqrt%7B3%7D%20x%20%5Csqrt%7B7%7D" id="TexFormula1" title="\frac{1}{3}\sqrt{21}-\frac{2}{3}\sqrt{3} x \sqrt{7}" alt="\frac{1}{3}\sqrt{21}-\frac{2}{3}\sqrt{3} x \sqrt{7}" align="absmiddle" class="latex-formula"> A. $-\frac{1}{3}\sqrt{21}$ B. $\frac{2}{3}\sqrt{21}$ C. $\frac{2}{3}\sqrt{18×7}$ D. $-\frac{1}{3}\sqrt{63}x\sqrt{7}$

Answer 1

Answer:

-1/3 sqrt(21)

Step-by-step 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)

Answer 2

Answer: Choice A)  $-\frac{1}{3}\sqrt{21}$

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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).