Help with square roots please?

Question

Ok so I was given homework on my summer break, right now im working on math. Its been awhile since Ive done these kind of problems so if someone could double check my answers for me that would really be nice.They all deal with simplifying.

1) (2 sqrt6)^2
My answer: 24

2) (sqrt6)(sqrt3)
My answer: 3 sqrt2

3) sqrt3/sqrt16
My answer: sqrt3/4

4) 8 sqrt5/sqrt4
My answer: 8 sqrt5/2

5) sqrt2/sqrt5
My answer: sqrt10/5

6) 3/sqrt12
My answer: sqrt12/4


Thanks!

Everybody is giving me different answers. :( Im confused

Answer 1

All are correct, you can simplify your answers in 4 and 6 further:

4. can be simplified further:
(8 * SQRT(5))/2 =
4 * SQRT(5)

6. can be simplified further:
SQRT(12)/4 =
SQRT(4 * 3)/4 =
(2 * SQRT(3))/4 =
SQRT(3)/2

Answer 2

Your answers are all correct, but they could confuse some people. For example sqrt12/4 could be interpreted as sqrt(12/4) = sqrt (3). It is best to write your answer as sqrt(12)/4, so that it is always clear what you are taking the square root of. sqrt4/2 could be sqrt(4)/2 = 1 or sqrt(2).

Answer 3

1) is correct: (2*sqrt(6))^2 = 2^2 * sqrt(6)^2 = 4 * 6 = 24

2) is correct: sqrt(6) * sqrt(3) = sqrt(6*3) = sqrt(18) = sqrt(9*2) = sqrt(9) * sqrt(2) = 3 * sqrt(2)

3) is correct: sqrt(3) / sqrt(16) = sqrt(3) / sqrt(4*4) = sqrt(3) / 4

4) is not correct: 8 * sqrt(5) / sqrt(4) = 8 * sqrt(5) / sqrt(2*2) = 8 * sqrt(5) / 2 = (8 / 2) * sqrt(5) = 4 * sqrt(5) (the problem was doing the further reduction of 8/2)

5) is correct: sqrt(2) / sqrt(5) = sqrt(2) * sqrt(5) / sqrt(5) * sqrt(5) = sqrt(2*5) / sqrt(5*5) = sqrt(10) / 5

6) is not correct: 3 / sqrt(12) = 3 / sqrt(4*3) = 3 / sqrt(2*2 * 3) = 3 / {sqrt(2*2) * sqrt(3)} = 3 / {2 * sqrt(3)} = 3 * sqrt(3) / {2 * sqrt(3) * sqrt(3)} = 3 * sqrt(3) / {2 * sqrt(3*3)} = 3 * sqrt(3) / {2 * 3) = 3 * sqrt(3) / (3 * 2) = sqrt(3) / 2 (you can also see it doing it your way, with sqrt(12) needing further reduction: sqrt(12) = sqrt(4*3) = sqrt(2*2 * 3) = sqrt(2*2) * sqrt(3) = 2 * sqrt(3) and dividing the 2/4 * sqrt(3) to get 1/2 * sqrt(3) or: sqrt(3) / 2)


All of them were correct as far as they went. Two just needed the further reduction/simplification.

Answer 4

You did well.
2) Should be sqrt(2)
4) Could be 2sqrt(5)
6) Could be sqrt(3)/2

Answer 5

#1 and 2 are right, but #3 should be 4sqrt3, #4 should be 16sqrt5, #5 should be sqrt10, and #6 should be 3/(2sqrt3).

If you need any help figuring out why these are the answers, just e-mail me, but you got the first two, and they're all based on the same principle, so if you just think about it a little you should get it.

Answer 6

1) correct
2) correct
3) correct
4) 8sqr[5]/sqr[4] x sqr[4]/sqr[4] = 8sqr[20]/4 = 2sqr[4*5] = 4 sqr[5]
5) sqr[2]/sqr[5] x sqr[5]/sqr[5] = sqr[10]/5
6) 3/sqr[4*3] = 3/(2sqr[3]) x sqr[3]/sqr[3] = 3sqr[3]/6 = sqr[3]/2