please help me with a homework problem?

Question

√12 -5 √-3 + (8- √-27=

the square root of 12 minus 5 squre root of negative 3 plus (square root 8 minus square root of negative 27

Please tell me how to do this problem and help me solve thanks.

Answer 1

So deal with the negative square roots first, then add together what has the same numbers under the square root. Break down what's under the square root into what can be multiplied to make that number. Such as
(-27) = -1 * 3 * 9
Do this for each square root to reduce them.

Remember that √-1 = i

√12 - 5√-3 + √8 - √-27 =

√12 - 5√(-1*3) + √8 - √(-1*3*9) =

√(4*3) - 5i√3 + √(4*2) - 3i√3 =

2√3 - 5i√3 + 2√2 - 3i√3 =

Now add the same numbers under the square roots together. Otherwise, they stay separate.

= 2√3 - 8i√3 + 2√2

Last, you can also get the front two factors together by factoring out the √3 from each.

= √3(2 - 8i) + 2√2


PS in your question it says (8 but then reads in words as the square root of 8, so I used the √8

Answer 2

We can use the imaginary number i =sqrt(-1) to make it less forbidding:
sqrt(12)- 5i sqrt(3) + 8 - i sqrt(27)
We can combine square roots ONLY if the same arguement is in the square roots. We note that 12=4*3 and 27=9*3, and that 4 and 9 are squares. Then........
2 sqrt(3)- 5i sqrt(3) -3i sqrt(3) +8
sqrt(3) [2-8i] + 8

Answer 3

square root of 12 is equal to sqaure root of 3 multiplied by the sqaure root of 4
the square root of 4 is eqaul to 2
try square root of 27 = sq root of 3 X sq root of 9
sq root of 9 = 3

so the question should look like this
(sq rt 3 X 2) - (5 X sq rt -3) + 8 - sq rt3 X 3
(2 rt 3 - 5 rt -3 ) + 8 - 3 rt 3
(2 rt3 - 5 rt -1 X rt 3 - 3 rt 3 + 8
2 rt 3 + 5 rt3 - 3 rt3 + 8
4 rt 3 + 8
this is your answer