more help please.

[j9vo2]

How do I do this problem?

simplify (20)^1/2.. it looks easy but I have no idea.

also....

simplify and rationalize the denominator: 8/[6+(2y)^1/2
do i multiply by 6+(2y)^2? is(2y)^1/2 the same as the sqrt of 2y?

how do i get started with this.. I got the first step.. I think, but not sure what to do after that.. -6x=3x^2-2

I got 3x^2+6x-2 = 0
do i divide everything by 3? then do the quadratic formula?

is this the correct answer for this one? x^2+-3x+3

this is what i did: -x^2-3x+3=0
-(-3) +/- sqrt (-3)^2-4(-1)(3)/2(-1)
3 +/- sqrt 9+12/-2

3 +/- sqrt 21/-2 answer.. is this the same as 3 +/- (21)^1/2?

 

[stapel]

Your formatting makes your post difficult for me to interpret. I have numbered your exercises as best I can....

1) Simplify "(20)^1/2"

I will guess that this reads "Simplify 20^1/2". If so, remember that "(something) to the one-half power" means the same as "the square root of (that thing)".

2) Simplify "8/[6+(2y)^1/2"

I'm sorry, but you have an unmatched grouping symbol. Please reply with clarification.

3) -6x=3x^2-2

What are the instructions? Are you solving? If so, by what method, or is the method up to you?

4) is this the correct answer for this one? x^2+-3x+3

I don't know. What's the question?

Please reply with clarification. When you reply, please include all of the steps you have done thus far.

Thank you.

Eliz.

 

[j9vo2]

Sorry about that.


1. simplify: square root of -20.. so would I do the square root of 4 and the square root of 5 and multiply them together? if so, then would the answer be: -5i sqrt-2?

2. 8 divided by 6+ sqrt 2y


3. -6x=3x^2-2 (solve by completing the square)


4. solve using the quadratic equation formula: x^2=-3x+3

these are is the steps that i took:

-x^2-3x+3=0
-(-3) +/- sqrt (-3)^2-4(-1)(3)/2(-1)
3 +/- sqrt 9+12/-2

 

[stapel]

1) Simplify \(\displaystyle \sqrt{-20}\)

To simplify the square root of a negative, one takes the "sqrt[-1]" out as an "i". This means that there is no longer any "minus" sign inside the radical. That's the point of the "i".

Also, 20 does not equal 5×5×2. Check your factorization.

2) Simplify \(\displaystyle \frac{8}{6\,+\,\sqrt{2y}}\)

(The above is what I am guessing your meaning to be. There is at least one other interpretation which easily could be made.)

To rationalize the denominator of the above expression, multiply top and bottom by the conjugate. Recall that the conjugate of an expression has the exact same terms, but the opposite sign in the middle.

3) Solve -6x = 3x² - 2 by completing the square.

The basic process for the completing the square is as follows:

. . . . .Get the variable terms on one side:
. . . . .ax² + bx = -c

. . . . .Factor out whatever is multiplied on the squared term:
. . . . .a(x² + [b/a]x) = -c

. . . . .Take half of the new coefficient on "x", and square:
. . . . .[1/2][b/a] = b/(2a), [b/(2a)]² = b²/(4a²

. . . . .Add this to both sides, making sure to account for "a":
. . . . .a(x² + [b/a]x + b²/(4a²) = -c + a(b²/(4a²)) = -c + b²/(4a)

. . . . .Write the variable side as a completed square:
. . . . .a(x + b/(2a))² = -c + b²/(4a)

. . . . .Solve by dividing through by "a", etc, etc.

4) Solve x² = -3x + 3 by the Quadratic Formula.

Without grouping symbols, I'm afraid I can't follow your work. It should be noted, however, that it is generally more helpful to start as:

. . . . .x² + 3x - 3 = 0

Then use the Formula....

. . . . .\(\displaystyle x\,=\,\frac{-b\,\pm\,\sqrt{b^2\,-\,4ac}}{2a}\)

...with a = 1, b = 3, and c = -3.

Eliz.

 

[j9vo2]

(1.) so the answer for the first one would be 2i sqrt 5 because 2.2.5 equals 20 and the "i" is taken out for the negative. am i correct?

(4.) I did the quadratic formula with a = 1, b= 3, and c = -3

-3 +/- sqrt (3)^2 - 4(1)(-3) divided by 2(1)

which equals -3 +/- sqrt 9 + 12 all divided by 2

which equals -3 +/- sqrt 21 all divided by 2

 

[j9vo2]

does anyone know if I did these correctly?? see my last post directly above. thanks.

 

[Unco]

(1.) so the answer for the first one would be 2i sqrt 5 because 2.2.5 equals 20 and the "i" is taken out for the negative. am i correct?
Correct

(4.) I did the quadratic formula with a = 1, b= 3, and c = -3

-3 +/- sqrt (3)^2 - 4(1)(-3) divided by 2(1)

which equals -3 +/- sqrt 9 + 12 all divided by 2

which equals -3 +/- sqrt 21 all divided by 2
x = ... Correct