Please help :(

N

Nataliebain

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Joined
Oct 25, 2014
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I'm really not sure where to post this, I have just started a home learn A level course and I'm a bit rusty
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Here are a few things I cannot get my head round ...

(3√2+5√3)^2 = (3√2+5√3)(3√2+5√3)
= 3√2(3√2+5√3)+5√3(3√2+5√3) - I get that we are multiplying what's outside the brackets with what's inside.
= 9√4+15√6+15√6+25√9 - I get that we can add the two 15√6 to make it 30√6
= 18+30√6+75 - Why has the 9√4 and the 25√9 been multiplied by 3?? Also why has the √9's disappeared?
I realise I'm probably being a bit thick but I haven't done maths in a while so this is really annoying me!

Also

5-√75/-5 = 5-√25x3/-5
= 5-5√3/-5 - I understand how I'm getting to here
= 5(1-√3)/-5 - why has the -5 on top
lb_icon1.png
turned into 1-?? I'm guessing we have divided something? Why and what?
= √3-1 - why has the -1 moved and what has happened to get rid of the 5 and the -5?

I know this is simple but I cannot fathom this out??
 
Nataliebain said:
(3√2+5√3)^2 = (3√2+5√3)(3√2+5√3)
= 3√2(3√2+5√3)+5√3(3√2+5√3) - I get that we are multiplying what's outside the brackets with what's inside.
Click to expand...
Have you not learned how to multiply multi-term expressions? If not, try here. The process for multiplying radicals is is much the same.

Nataliebain said:
...= 5-5√3/-5 - I understand how I'm getting to here
= 5(1-√3)/-5 - why has the -5 on top
lb_icon1.png
turned into 1-?
Click to expand...
They factored out the common factor of 5, taking it out front. ;)
 
Thank you! I understand now, if I'm honest there isn't much learning material before it gives me practise questions so I'm having to search online for help :( it's been a long time since I studied so I'm just getting back into the swing of things.

The only other thing I'm struggling with is rationalising the denominator, I am ok doing simple ones but

√5-√2/√5+√2 i know I am multiplying both top and bottom by √5-√2 but again it's just not sinking in :(

ive been trying to find somewhere online with simpler ways of understanding
 
Nataliebain said:
5-√75/-5 You need grouping symbols around the numerator.

= 5-√25x3/-5 See the top statement. You're doing algebra. I recommend you use an asterisk
instead of the "x," which looks like a variable. The radicand must be in grouping symbols.

= 5-5√3/-5 - I understand how I'm getting to here [/b]See the top statement.[/b]

= 5(1-√3)/-5 - why has the -5 on top
lb_icon1.png
turned into 1-?? I'm guessing we have divided something? Why and what?

= √3-1 - why has the -1 moved and what has happened to get rid of the 5 and the -5?
Click to expand...

Nataliebain, here are some extra steps to follow along. There are other routes instead
of this one:


(5 - √75)/-5

= [5 - √(25*3)]/-5

= (5 - 5√3)/-5

= 5(1 - √3)/-5

= (1 - √3)/-1

= (-1)(1 - √3)/[(-1)(-1)]

= (-1 + √3)/1

= -1 + √3

= √3 - 1





 
Thank you! I think I'm forgetting brackets and then confusing myself,

on this one I get to here and get stuck...

(√5-√2)/(√5+√2) x top and bottom by √5-√2 =
(√5^2)-√10-√10+(√2^2) on the top which I know is 7-2[FONT=AppleSDGothicNeo-Regular, lucida grande, tahoma, verdana, arial, sans-serif, Segoe UI Emoji, Segoe UI Symbol, NotoColorEmoji, EmojiSymbols, Symbola, Noto, Android Emoji, AndroidEmoji, Arial Unicode MS, Zapf Dingbats, AppleColorEmoji, Apple Color Emoji]√10 but on the bottom I get stuck...
([/FONT]√5^2)-√10-√10-(√2^2) ... I know the bottom should be 5-2=3 but I can't understand why the √10^2 is on the top but not on the bottom?

i feel so stupid right now!
 
Nataliebain said:
Thank you! I think I'm forgetting brackets and then confusing myself,

on this one I get to here and get stuck...

(√5-√2)/(√5+√2) x top and bottom by √5-√2 =
(√5^2)-√10-√10+(√2^2) on the top which I know is 7-2√10 but on the bottom I get stuck...
(√5^2)-√10-√10-(√2^2) ... I know the bottom should be 5-2=3 but I can't understand why the √10^2 is on the top but not on the bottom?

i feel so stupid right now!
Click to expand...

You do NOT have √10^2 on the top (numerator). You have (√10 + √10 =) 2 * √10

in the bottom denominator (bottom), you have,

(√5^2) - √10 + √10 - (√2^2)

notice that the √10 's in the bottom have opposite signs ( + and -) so those turn into 0 (because -a + a = 0)
 
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