simplify..

B

bobisaka

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(10 -√75) / 5

(10 - √25*3) / 5

(10 - 5√3) / 5

(10*2 - 5*2√3)/5 <============ THIS IS WHERE I GET LOST

(20 - 10√3)/5

(4 - 2√3)

2√3 <========== HOW DO WE GET IT TO BECOME 2-√3
 
bobisaka said:
(10 -√75) / 5

(10 - √25*3) / 5

(10 - 5√3) / 5

(10*2 - 5*2√3)/5 <============ THIS IS WHERE I GET LOST

(20 - 10√3)/5

(4 - 2√3)

2√3 <========== HOW DO WE GET IT TO BECOME 2-√3
Click to expand...
At the line you point out, you multiplied the numerator by 2 without changing the denominator. That doubled the value of the expression.

There are several ways to write the work that are correct; what I would do is to divide both terms of the numerator by 5:

(10 - 5√3) / 5 = (10 / 5) - (5√3 / 5) = 2 - √3​

We can distribute the division, because dividing a sum or difference by something just divides each term.

At the last step, when we divide 5√3 by 5, we are in effect removing a factor of 5, leaving just the radical in this case.
 
bobisaka said:
(10 -√75) / 5

(10 - √25*3) / 5

(10 - 5√3) / 5

(10*2 - 5*2√3)/5 <============ THIS IS WHERE I GET LOST
Click to expand...
Why did you multiply the numerator by 2?

If you had written this as an equation, your error would have been apparent.

[MATH](10 - \sqrt{75}/5 = x\implies [/MATH]
[MATH](10 - \sqrt{25 * 3})/5 = x \implies[/MATH]
[MATH](10 - 5\sqrt{3})/5 = x \implies [/MATH]
[MATH]2(10 - 5\sqrt{3})/5 = 2x \implies[/MATH]
[MATH](20 - 10\sqrt{3})/5 = 2x \implies[/MATH]
[MATH]4 - 2\sqrt{3} = 2x.[/MATH]
Now divide by 2 to get the correct answer

[MATH](4 - 2\sqrt{3})/2 = 2x/2 \implies [/MATH]
[MATH]x = 2 - \sqrt{3}.[/MATH]
Your multiplying by 2 led you astray. Why did you think it was helpful?
 
JeffM said:
[MATH]x = 2 - \sqrt{3}.[/MATH]
Click to expand...


The way I calculate the final answer:

(4−2√3)/2=2x/2 ⟹

x = 2-1√3 <==== is this the same as x=2−√3


I am confused as to how the '-2√3' becomes '-√3'.
 
[MATH]\dfrac{10 - \sqrt{75}}{5} = \dfrac{10}{5} - \dfrac{\sqrt{75}}{5} = 2 - \dfrac{\sqrt{25 \cdot 3}}{5} = 2 - \dfrac{5\sqrt{3}}{5} = 2 - \dfrac{\cancel{5}\sqrt{3}}{\cancel{5}} = 2 - \sqrt{3}[/MATH]
 
skeeter said:
[MATH]\dfrac{10 - \sqrt{75}}{5} = \dfrac{10}{5} - \dfrac{\sqrt{75}}{5} = 2 - \dfrac{\sqrt{25 \cdot 3}}{5} = 2 - \dfrac{5\sqrt{3}}{5} = 2 - \dfrac{\cancel{5}\sqrt{3}}{\cancel{5}} = 2 - \sqrt{3}[/MATH]
Click to expand...
Wow, thank you.
 
I agree that 4-2=2, however in 4-2sqrt(3) there is no subtraction of 2! You are subtracting 2sqrt(3) from 4, NOT 2!!
 
Last edited:
I had to search to find what Jomo is referring to, because he didn't quote you. It's here, in the OP:
bobisaka said:
(4 - 2√3)

2√3 <========== HOW DO WE GET IT TO BECOME 2-√3
Click to expand...
You appear to be make an order of operations error here, as if it said (4 - 2)√3 rather than 4 - 2√3.

The multiplication is done first, so you subtract all of 2√3 from 4, rather than subtracting 2 from 4 and then multiplying by √3.
 
bobisaka said:
(10 -√75) / 5

(10 - √25*3) / 5

(10 - 5√3) / 5

(10*2 - 5*2√3)/5 <============ THIS IS WHERE I GET LOST

(20 - 10√3)/5

(4 - 2√3)

2√3 <========== HOW DO WE GET IT TO BECOME 2-√3
Click to expand...

2√3 = 2 (multiplied by) √3

It is different from the way we consider "mixed fractional" numbers like 2½ or 3.5, where we mean:

2½ = 2 (added to) ½...................... or.........

3.75 = 3 + 0.75
 
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