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## Math help please

This is a discussion on Math help please within the General Off Topic+ forums, part of the QJ.net Forum Miscellaneous category; Can anyone help with these questions? I've had a look, but I really don't understand. Thanks Express these as single ...

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1. ## Math help please

Can anyone help with these questions? I've had a look, but I really don't understand. Thanks

Express these as single square roots (for example √k)

5√3
9√7

Simplify these by rationalising the denominators

5/√3 (The / means over e.g 1/4 would be one quarter)
7/√6
6/√2
4/7 - √5

Write these in the form a + b√c

(√3 + 2)²
(√7 - 5)²
(√3 + √2)(√2 - √3)
(2√5 + 3√2)(2√2 - 3√5)

Please could you help me answer them? I'm really stuck.

2. 1) /27 = /9 x 3

umm ****, thats the only step I remember. lol

3. Write these in their simplest form:

1) √27
1) Ok, first we find everything that makes 27:

1 x 27
3 x 9

To find out which we use, we find the sum that has a square root number in it:

1 x 27 = No.
3 x 9 = Yes. The number 9 (3 x 3 = 9).

So we use the sum '3 x 9'.

Now, we do:

√27 = √3x9
= √3 x √9
= 3√3

What I did above:

3 cannot be simplified so we put it as √3. 9 can be simplified so we simplify it to it's lowest form, which is 3. We then put the simplified number in front of the √3, to make 3√3.

Express these as single square roots (for example √k)

5√3
9√7
Sorry, can't remember

Simplify these by rationalising the denominators

5/√3 (The / means over e.g 1/4 would be one quarter)
7/√6
6/√2
4/7 - √5
Also can't remember

Write these in the form a + b√c

1) (√3 + √2)(√2 - √3)
1) First we simplify by dividing the first bracket, and then we use the second bracket in both sums:

Sum 1:
√3(√2 - √3)

Sum 2:
√2(√2 - √3)

Now we attach both sums together:

√3(√2 - √3) + √2(√2 - √3)

The plus that we put between both sums comes from the plus found in the first pair of brackets (I.E.: (√3 + √2))

I'm afraid we haven't gotten past this point in the sum yet in my class, sorry.

4. Originally Posted by -Dan-
Can anyone help with these questions? I've had a look, but I really don't understand. Thanks

Write these in their simplest form:

√27 = sq (3 * 9) = 3 sq 3
3√20 = 3 * sq (4 * 5) = 6 sq 5
All I felt like doing

5. I did the sums I knew, hope it helped.

6. Yeah, it helped thanks. Still stuck on the ones in my first post

7. Originally Posted by -Dan-
Can anyone help with these questions? I've had a look, but I really don't understand. Thanks

Express these as single square roots (for example √k)

5√3=sqrt(25*3)
9√7=sqrt(81*7)

Simplify these by rationalising the denominators

5/√3=5sqrt(3)/3
7/√6=7sqrt(6)/6
6/√2 = 6sqrt(2)/2
4/7 - √5 = (4sqrt5) - 35)/(7sqrt(5))

Write these in the form a + b√c

(√3 + 2)²
(√7 - 5)²
(√3 + √2)(√2 - √3)
(2√5 + 3√2)(2√2 - 3√5)

Please could you help me answer them? I'm really stuck.
as for the last ones just do FOIL... im late for a date so i gotta go, ill do those when i get back if u havent figured it out.

8. OK, but I gotta go in 2 and a half hours.

9. I'm don't know anything about this, but you can always look in your textbook. They always have examples to help you.

10. k im back for like 5 mins.
-= Double Post =-
Originally Posted by -Dan-
Can anyone help with these questions? I've had a look, but I really don't understand. Thanks

Express these as single square roots (for example √k)

5√3
9√7

Simplify these by rationalising the denominators

5/√3 (The / means over e.g 1/4 would be one quarter)
7/√6
6/√2
4/7 - √5

Write these in the form a + b√c

(√3 + 2)²= 7 +4sqrt(3)
(√7 - 5)² = 32 - 10sqrt(7)
(√3 + √2)(√2 - √3) = 5 + 0sqrt(0) = 5
(2√5 + 3√2)(2√2 - 3√5) = -18 - 5sqrt(10)

Please could you help me answer them? I'm really stuck.
yup yup... i love being smart :)
-= Double Post =-
if you need explanations on how to do all this then contact me on aim or msn or yim or pm closer to.....7 or 8 EST

11. Originally Posted by -Dan-
Can anyone help with these questions? I've had a look, but I really don't understand. Thanks

Express these as single square roots (for example √k)

5√3 (multiply 5 in twice) √75
9√7 √567

:)

12. these are all the answers along with work and an explanation hope it helps.
Originally Posted by -Dan-
Can anyone help with these questions? I've had a look, but I really don't understand. Thanks

1.Express these as single square roots (for example √k)

a.5√3
b.9√7

2.Simplify these by rationalising the denominators

a.5/√3 (The / means over e.g 1/4 would be one quarter)
b.7/√6
c.6/√2
d.4/7 - √5

3.Write these in the form a + b√c

a.(√3 + 2)²
b.(√7 - 5)²
c.(√3 + √2)(√2 - √3)
d.(2√5 + 3√2)(2√2 - 3√5)

Please could you help me answer them? I'm really stuck.
i numbered them for easy reference:
1a. √75 (since its 5√3, 5 is just the root of 25. turn 5 back into √25 and then multiply √25 and √3. same thing with 1b.)
1b. √567
2a.5√3/3 (what you have to do with these is multiply by 1. now my 1 i mean the radical in the denominator over itself. for example x/x is 1 since any number over itself is one. so since u multiply by 1 you r not changing the answer. so what you do is multiply 5/√3 by (√3/√3) since that doesnt change the value of the fraction then you go on to simplify since √3 "times" √3 is 3, the denominator is now rationalized. do the same with all of them.)
2b. 7√6/6
2c.6√2/2
2d. 7+√5/11 (what you do here is multiply by whats called a conjugate. a conjugate is the same thing as the denominator but you change the sign of the second term. for example the conjugate of x-√x is x+√x. so the conjugate of (7-√5) is (7+√5). now like in the above questions you wanna multiply by 1 so you multiply 4/(7-√5) by (7+√5/7+√5).)
3a. 7+2√3. (here its just like doing foil method with quadratic roots. what you do is (√3+2) "times" (√3+2). you multiply the first terms then the outer terms, then the inner terms and then the last term. this will get you 3, 2√3, 2√3, and 4. you now combine like terms and get your answer. same with the rest.)
3b. 32-10√7
3c. 2√6. (here you will end up with (√6+√6). now say you were to end up with (√x+√x) you would not do √2x. instead you would end up with 2√x. same thing applies to the above. (√6+√6) adds up to 2√6.
3d. -18-5√10. here you do something a little different. after you multiply everything out you will get the terms 4√10, -6√25, 6√4, -9√10. when you combine the like terms you are left with -5√10-6√25+6√4. but you know √25 and √4 are square roots. so u simplify √25 and √4 to 5 and 2. now you get 5 and 2 so the new term becomes -5√10-(6 "times" 5)+(6 "times" 2). simplify all that and you get 4√10 -30+12. now combine -30 and 12 and you get -18 thus making the answer (-18-5√10).

13. He doesn't listen in class, obviously.

14. I do listen in class, but I missed this on Friday because my flu got worse, so I had to stay off.

15. If you missed class then you wouldn't have received the homework.

16. The teacher gave it to a friend of mine who lives nearby.

17. You've been caught out now, don't try to argue now unless you have Bird Flu.

18. Originally Posted by -Dan-
The teacher gave it to a friend of mine who lives nearby.
Hmmm.... I think we're gonna have to call in Sherlock Holmes to solve this one.

19. Don't believe me; Do I give a f**k?

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