Question

Expand this expression, (3-√5)^2 in the form of a + b√c and where a,b,c are integers.

Answer 1

lets say 3 = a and sqrt(5) = b
then the expression becomes (a-b)^2
do you know the formula for that?

Answer 2

Well, I understand that I should do (3-√5)(3-√5)..
1) 3 x 3 = 9
2) 3 x -√5 = -3√5
3) -√5 x 3 = -3√5
4) -√5 x - √5 = 2√5

So thats 9 -3√5 -3√5 + 2√5, But I dont know If i have done that correct.

Answer 3

why is \[\sqrt5 \times \sqrt5 = 2\sqrt5\]
?

Answer 4

Oh, I dont know- Is it 25?, I keep forgetting that..

Answer 5

no. do you know what square root means?

Answer 6

well, yeah- but i don't know how I would approach this, timing 2 square roots together because I forget :l

Answer 7

go to www.google.com
type in sqrt(5) and see what number you get. paste it here.

Answer 8

sqrt(5) = 2.23606798 - ah, yes- its a surd, i think.

Answer 9

okay good.
now go to google again
and this time type in 2.23606798 * 2.23606798 and paste what number you got.

Answer 10

AH YES :P- I remember!, its about 5, so that means √5×√5√ = 5 :P

Answer 11

yup. square root of a number is another number such that when you multiply that number by itself, you get the original number

Answer 12

if x times x gives you a number y, that means that x is the square root of the number y
and consequently, y is the square of x.
we call it square because that is how we find the area of a square.
The area of a square is nothing by the side times the side.

Answer 13

if you have a number x such that x times x times x yields a number y, then y is the cube of x and x is the cube root of y.
we call them cubes and cube roots because to find the volume of a cube you multiply the side by itself thrice.

Answer 14

Ah yes, I understand surds and those now :)- Thank you very much, and i assume the rules of BIDMAS such as -5√×5√ = -5 and -5√×-5√ = 5?

Answer 15

:)