How do you simplify #3+sqrt2-7+3sqrt2#?

1 Answer
Jan 13, 2017

Answer:

See the full simplification process below:

Explanation:

First, we can group like terms:

#3 + sqrt(2) - 7 + 3sqrt(2) -> 3 - 7 + sqrt(2) + 3sqrt(2)#

We can now group like terms:

#3 - 7 + 1sqrt(2) + 3sqrt(2) -> -4 + (1 + 3)sqrt(2) ->#

#-4 + 4sqrt(2) -> 4(-1 + sqrt(2)) -> 4(sqrt(2) - 1)#

We can now take the square root of 2 and calculate the value of the expression:

#4(sqrt(2) - 1) = 4(1.414 - 1) = 4 xx 0.414 = 1.656# to the nearest thousandth.