Help with math? I need it done by tomorrow?

Question

Alright, this is actually for an exam thing, take home.. I need A LOT of help on it. Can someone help me out?!


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Answer 1

(6)
SQRT(36/49)

Okay - here you gotta use the property SQRT(a/b) = SQRT(a)/SQRT(b)

SQRT(36/49) = SQRT(36)/SQRT(49) = 6/7

(7)
SQRT(16x^2)
Again ... utilise the property SQRT(a.b) = SQRT(a).SQRT(b)

SQRT(16x^2) = SQRT(16).SQRT(x^2) = 4x

(8)
CubRT(-27)
What number times itself, times itself (again) gives -27
That's -3

(9)
SQRT(72x^5) = SQRT(72).SQRT(x^5)
= SQRT(2.4.9).SQRT(x.x^4)
= SQRT(4).SQRT(9).SQRT(2).SQRT(x^4).SQRT(x)
= 2.3.SQRT(2).x^2.SQRT(x)
= 6x^2.SQRT(2).SQRT(x)
= 6x^2.SQRT(2x)

(10)
CubRT(32.x^5.y^6)
= CubRT(2^5.x^5.y^6)
= CubRT(2^3.2^2.x^3.x^2.y^6)
= CubRT(2^3).CubRT(2^2).CubRT(x^3).CubRT(x^2).CubRT(y^6)
= 2.CubRT(4).x.CubRT(x^2).y^2
= 2.x.y^2.CubRT(4.x^2)

(11)
27^ (1/3)

This is the same as CubRT(27)

which is 3

as 3.3.3 = 27

(12)
16^ (1/2)
This is the same as SQRT(16)
I'm sure you can go from there

(13)
4^ (2/3)
This is the same as CubRT(4^2)
or CubRT(16)

(14)
SQRT(-36)
= SQRT(-1.36)
= SQRT(-1). SQRT(36)
= 6.SQRT(-1)
Now ... have you learned about imaginary numbers and complex numbers yet? They define an imaginary number i = SQRT(-1)

If you're not up to this bit of maths, then you say there is no real SQRT(-1) which is true and call it quits there.

(15)
2.SQRT(15).SQRT(6)
= 2.SQRT(3.5.2.3)
= 2.SQRT(10.9)
= 2.3.SQRT(10)
= 6.SQRT(10)

(16)
CubRT(6x).CubRT(9.x^3.y^7)
= CubRT(2.3.x.3.3.x^3.y^7)
= CubRT(3^3.x^3.y^6.2.x.y)
= 3xy^2CubRT(2xy)

(17)
SQRT(3)(4 + SQRT(3))
Expand brackets
= SQRT(3).4 + SQRT(3).SQRT(3)
= 4.SQRT(3) + 3

(18)
(2+SQRT(6))(4-SQRT(6))
use F.O.I.L. (Firsts outers inners lasts)
= 8+4SQRT(6)-2SQRT(6)-SQRT(6)^2
= 8+2SQRT(6)-6
= 2 + 2.SQRT(6)

(19)
SQRT(-2).SQRT(-12)
= SQRT(-1.2.-1.2.2.3)
= SQRT(2^2.6) as the -1 time -1 = 1
= 2.SQRT(6)

(20)
(3+2i)(1+i)
Looks like you HAVE done i = SQRT(-1)
Use FOIL
= 3 + 2i + 3i + 2i^2
= 3 +5i -2 because SQRT(-1).SQRT(-1) = -1
= 1 + 5i

==={Phew! A little rest break before the next page}===

Okay, back to it

(21)
SQRT(11/6) = SQRT(11)/SQRT(6) I'm not sure which you'd consider simpler form.

(22)
4/SQRT(2) = SQRT(16/2) = SQRT(8) = SQRT(2.2.2)
= 2.SQRT(2)

(23)
2/CubRT(3) = CubRT(8/3)

(24)
4/1-SQRT(2)

Well, this either says (4/1) - SQRT(2) which is 4-SQRT(2) or 4/(1-SQRT(2)) which is a little difficult to simplify further, I think.

(25)
(3+2i)/(2+i) again looks to be in simplest form unless it was meant to be 3+ (2i/2) + i = 3+2i

(26)
3.SQRT(6) - CubRT(2) - 5.SQRT(6) + 8.CubRT(2)
= 7CubRT(2) - 2.SQRT(6)

(27)
SQRT(20) + SQRT(80) + SQRT(45)
= SQRT(2.2.5) + SQRT(2.2.2.2.5) + SQRT(3.3.5)
= 2SQRT(5) + 4SQRT(5) + 3SQRT(5)
= 9SQRT(5)

(28)
(3+5i) - (6-2i)
= 3-6 +5i+2i
Remember that a negative times a negative is a positive
= -3 + 7i

(29)
SQRT(y+1) + 5 = 8
This can be solved just like most other algebra

SQRT(y+1) = 8-5 = 3
y+1 = 3^2
You have to square both sides

So ...
y+1 = 9

etc.

(30)
CubRT(x) + 5 = 3
CubRT(x) = 3-5
x = (-2)^3

Or did you mean to say
CubRT(x+5) = 3
?

You can solve that one easy.

(31)
SQRT(y-3) + 2 = 0
SQRT(y-3) = -2

Square both sides and you're away

Answer 2

Why don't you just look up your book some examples on the "complex number system". Look for a problem similar to the ones you are given ... sit down and just do the work.

Answer 3

Well...seems to me that the first thing you need to do is turn off the damn computer and get to work.

Answer 4

I'm your teacher... and you have just recieved an F.
I know who YOU ARE!