Simplifying surds

[loz58]

How do you simplify this question?
(3+√5)(3-√5)
Thank you

[nix-j-c]

hangon 1 sec . . . i've done 1 lesson on surds and loads on multiplying brackets

. . .

i think the answers 9-#25

p.s. i cant find square root button so it means 9 minus swuareroot of 25

i could be completely and uttterly wrong but i had a go and im not meant 2 know about surds until 2 years time but 2 get lvl 8 in sats i needed 2 do surds, triganometry circle theroms and algebraic fractions

i could b completely wrong btw

[gen2]

No that expression you posted is the factorisation of the difference of two squares.

= 3 squared minus √5 squared

= 9 - 5

= 4

[derrynoose]

I can't access a square root sign so please read # as a root sign.
Multiply top and bottom of your fraction by 3+#5. This gives a top line of (3+#5)(3+#5) and a bottom line of (3-#5)(3+#5). Top line simplified gives 14+6#5. Bottom line simplified gives 9-5 through difference of two squares, ie 4. Answer is 14/4 +6#5/4 or 7/2 +3#5/2.
Generally, if bottom line is a+#b multiply top and bottom by
a-#b. If bottom line is a-#b multiply top and bottom by a+#b.
In technical terms you multiply above and below by theconjugate of the bottom line.
How do I type the square root sign?

[gen2]

derrynoose

a) I don't see any fraction in the question?

b) for √ (and other symbols) copy and paste from Word Processor
Or in this case I copied and pasted from the questin at the top.

eg

√ x� = x

☺☺☻☻

[Jonvisnick]

second answer is right
9+3√5-3√5-5 = 9-5 =4

[derrynoose]

Thanks Gen2 and Johnvisnick. I made the schoolboy mistake of not reading the question carefully.
Maybe my answer will be of value to you, loz58, if you move on to rationalising surds!
Thanks also to Xerus .

[mibn2cweus]

Isn�t this simply a variation on the difference of two squares?

(x-y)(x+y) simplifies to x2-y2

In the expression in question, substituting 3 for x and √5 for y

(3 + √5) (3 - √5) becomes

3� - √5�

and since the square of a square root normalises
(√5� = 5) we get

3� - 5

Here�s a visualization of a� - b� = (a - b) (a + b)

[loz58]

well when i had a go at the question and i got the same answer as Jonvisnick and Gen2, so you saying that its 4, gives me a bit of confidence, but i just hope it right, thank you for all your help