Question #fe9b0

1 Answer
Apr 3, 2017

Answer:

See below:

Explanation:

If the question is:

#(sqrt(5) - 6)^2#

Then you can rewrite this as:

#(sqrt(5) - 6)(sqrt(5) - 6)#

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(sqrt(5)) - color(red)(6))(color(blue)(sqrt(5)) - color(blue)(6))# becomes:

#(color(red)(sqrt(5)) xx color(blue)(sqrt(5))) - (color(red)(sqrt(5)) xx color(blue)(6)) - (color(red)(6) xx color(blue)(sqrt(5))) + (color(red)(6) xx color(blue)(6))#

#5 - 6sqrt(5) - 6sqrt(5) + 36#

We can now combine like terms:

#5 + 36 + (-6 - 6)sqrt(5)#

#41 - 12sqrt(5)#

If you want this as a single number, #sqrt(5) = 2.236# rounded to the nearest thousandth.

Substituting this in gives:

#41 - (12 xx 2.236)#

#41 - 26.833#

#14.167# rounded to the nearest thousandth.