How do you evaluate #\sqrt { \frac { ( 6) ( 136^ { 2} ) + ( 21) ( 185^ { 2} ) } { 7+ 21+ 2} }#?

1 Answer
Ryuu
Aug 2, 2017

Simplify the terms in the numerator and denominator and continue using BEDMAS.

Explanation:

This is pretty easy. We can just input all of this into a calculator and use brackets accordingly, but to avoid confusion, I'll do it one step at a time.

First step, is simplify the numerator and denominator.

For numerator:

We'll simplify the first 2 terms (the terms before the #+#).

#6*136^2#

#=6*18496#

#=110976#

And then the next two terms.

#21*185^2#

#=21*34225#

#=718725#

We add the two values together...

#110976+718725#

#=829701

So now we have...

#sqrt(829701/(7+21+2))#

For denominator:

Just add the 3 terms.

#7+21+2=30#

So now we have...

#sqrt(829701/30)#

We can simplify the fraction to #276567/10#.

Thus, we get...

#sqrt(276567/10)#

If we use the square root function, we get a decimal. Due to inaccuracy, I will leave the solution there.

If you want, you can carry on with the operation (just do #276567-:10#, then hit the #sqrt# function and then #=#. You should get #~~166.303#).

Hope this helps :)

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