A couple of questions about surds...?

Question

1) 3 x 1/4? I'm being a bit silly but is this 3/4 or 3/12?

How do you add surds, I'm slightly confused!

2) 2 root 2 + root 2? Would that be 2 root + 1?

3) root 2 + root 2?

Thanks. :o)

Answer 1

I think it's
1). 3 x 1/4 is like 3/1 x 1/4 which = 3/4.
2). 2 root 2 + root 2 is like you have two already and you add another so that would = 3 root 2.
3). root 2 + root 2 is like one thing plus another so = 2 root 2.
It's kinda like treating them like objects so you just treat the number in front as the number you already have.
Hope that helps.

Answer 2

Okay I think you might be confusing yourself here, first thing to remeber about maths is that at a basic level it is purely logical. Secondly that mathematicians are lazy, if there is an easy way of writing something or solving something then they have thought of it

They even came up with their own symbolic language, and then invented rules so it all fitted together....

1) Working with fractions is easy stuff when you decipher what it means:
Two ways of looking at this particular problem

a) Mathematicians use the x sign to mean "of things that are "
so the question 3 x 1/4 should be read as

3 of things that are 1/4= ( so three "piles " of things that are 1/4 is 3/4)

b) change both sides into fractions
Remember that 3 is the same as 3/1

so we get 3/1 x 1/4

multiply the tops 3 x 1 = 3
multiply bottoms 1 x 4 = 4

giving us 3/4

2) again read the question long hand and remember rules

2 root 2 is the shorthand way of writing "2 of the things that are root 2"
root 2 is the shorthand way of writing " 1 of the things that are root 2"

it should know be obvious if you ask yourself how many root 2 do you have that you have three of them

so the answer is 3 root 2

3) Think about it!!! if you cant look at the answer above

Answer 3

1. 3/4

2. 4 root 2

3. 2 root 2

Answer 4

1) 3 x (1/4) = (3/1) x (1/4) = 3/4
You multiply the top number with the top number and the bottom with the bottom number.
And 3 is the same as 3/1.

2) 2 root 2 + root 2 = 3 root 2
Similar to 2 apples + 1 apple = 3 apples where apples = root 2 which has a value of 1.414 (to 3 dec pl).

3) root 2 + root 2 = 2 root 2
Same explanation as above.

Answer 5

1. 3/4
2. 3 root 2
4. 2 root 2

Answer 6

1) 3 x 1/4
3/1 x 1/4 [To multiply fractions, simple multiply numerator by numerator; denominator by denominator]
= (3x4) / (1x4)
= 3/4

2) 2 root 2 + root 2
[Simply treat "root 2" as if it were, for example x]
[So, 2x + x = 3x]
= 3 root 2

3) root 2 + root 2
[Same as before, treat it as an object, rather than the square root of something]
[x + x = 2x]
= 2 root 2

It's simple when you look at it this way! I hope this helps!

Answer 7

1)
think of it as 3/1 x 1/4 then multiply the two numerators and the two denominators
so you have 3 x 1/4 = 3/1 x 1/4 = (3x1)/(1x4) = 3/4

2)
consider it as x=root 2
then you have 2x+x = 3x = 3 root 2

3)
same as above
x+x = 2x = 2 root 2

Answer 8

1) 3*1/4=3/4 or 0.75
2) 2 root 2 + root 2 = 3 root 2
3) root 2 + root 2 = 2 root 2

Don't worry, you're not being silly!

Please pick me for best answer!

Answer 9

2.itwill be 3 root 2
3.it will be 2 root 2

Answer 10

first part is 3/4 been that long since i was at school dont remember roots so cant help you there sorry