Fractions and roots I have this problem: \frac{\sqrt{18}+\sqrt{98}+\sqrt{50}+4}{2\sqrt{2}

Deven Livingston 2022-04-23 Answered
Fractions and roots
I have this problem:
18+98+50+422
I'm able to get to this part by myself:
152+222
But that's when I get stuck. The book says that the next step is:
15222+222
But I don't understand why you can take the 2 out of the original fraction, make it the numerator of its own fraction and having root of 2 as the denominator of said fraction.
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Answers (2)

alastrimsmnr
Answered 2022-04-24 Author has 18 answers

18+98+50+422=32+72+52+422=152+422
Now the standard procedure is to remove the radical in the denominator:
152+422=152+42222=152·2+4222·2=30+424=15+222
One can do it differently: set a=2, so you can write
152+422=15a+a4a3=15+a3a2=15+222
The final result can also be written by using a+bc=ac+bc so
15+222=152+2
Whether you want to do this last transformation depends on what you have to do with this number.

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ubafumene42h
Answered 2022-04-25 Author has 13 answers
To me the next obvious step is to remove the radical in the denominator so
152+222=15+22.
Personally I would stop there, but you could separate this into 152+22 or into 152+12 if you really wanted to.

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