Calculating triangle side

[Unregistered]

I am stuck on a problem with a triangle question

I have a right angled triangle with sides of 10√3 and (20√2)-10.
The question is to work out the hypotonese of it using exact values. The hypotonese is opposite the 90 degree angle.

[Grapper]

Use Pythagoras's theorem

i.e

hypotenuse = (10√3) + [(20√2)-10]

= 100(3) + [(20√2)-10][(20√2)-10]
square out the last bracket
= 300 + 400(2) - 200√2 - 200√2 + 100

= 300 + 800 - 400√2 +100

= 1200 - 400√2
factorise
= 400(300-√2)

so
hypotenuse = √[400(300-√2)]

= 20√(300 - √2)


Hope that helps

[Unregistered]

Thx it does help but for some reason my answer book says its

20√(3-√2)

Can it be simplified more or something like that?

[Unregistered]

Oh wait i found out where the difference is well atleast i think so

= 1200 - 400√2
factorise
= 400(300-√2)

shouldn't it be 400(3-√2)

Thx for your help that one annoyed me for ages lol.

[Grapper]

Your right. Silly typo.