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26 votes
26 votes
Select the correct answer.

Which expression is equivalent to √48x5, if x > 0?
OA. 12x³√3x
OB. 4x³√3
OC. 4x²√3x
OD. 12x²√

User Jose Rivera
by
2.6k points

1 Answer

21 votes
21 votes

Answer:

C

Explanation:

Comment

The square root of 48 is nowhere near 12. That means that A and D are wrong. On a test that's an important consideration because if you have to guess, you've just cut the possibilities down to 2.

So the answer must be B or C. Furthermore, you don't have to go to the trouble of factoring 48 to show that it is 4 sqrt(3). There's no other choice.

So what about x^5. 5 is an odd number. That means that one of the xs is left underneath the square root sign. That makes B incorrect. Without doing a calculation, I know that C is the answer.

Note

x^5 = x * x * x * x * x

The rule is for ever 2 factors that are the same, 1 factor is put in front of the square root sign and the other 1 is thrown out.

√x^5 = √x * x * x * x * x = x * x √x

Therefore the answer to the problem is 4 x * x√3 x = 4x^2√3x

User Shantanu Banerjee
by
3.1k points