Math surd problems & equations need some help !?

Question

Ok i have this maths assignment on surds and some of the questions are quite annoying.

For example I have this question: (sorry for the poor square root symbols)

..._........._......... __

_/2 + _/8 + _/50

......................................... _

And i thought the answer was _/60

is that right?

and i also have this other question:

..__.........__........___....... __

_/27 + _/20 - _/108 + _/45

i also need to show all working for everything

and finally the hardest question on my assingment is:

.....__.........__

8_/18 x 3_/3

____________

......._

16_/27

Any explanations bout anything or any suggestions would be great.

And just remember i need to show working so if someone could tell me how it works it would be greatly appreciated.

Thanks alot

Answer 1

No, you can't just add the numbers under the square roots. If you don't believe me, try checking:

sqrt 2 is about 1.4, sqrt 8 is about 2.8, sqrt 50 is about 7.1, right? So added together you get 11.3, but sqrt60 has to be less than 8.

What you need to do is factor out sqrt2 from all the numbers:

sqrt2 + sqrt(2x4) + sqrt(2x25)

Now, you CAN distribute the square root over multiplication, so that's

sqrt2 + (sqrt2 x sqrt4) + (sqrt2 x sqrt25)

sqrt2 + (sqrt2) x 2 + (sqrt2) x 5

Then add up all the sqrt2's and you have 8x sqrt2.

(8 x 1.4 = 11.2 so I was pretty close!)

Answer 2

The way you've done it's good but i don't get the last question :)