How do I answer these questions involving square roots?

Question

1) Simplify the expression √32 + √98

 

2) Solve the equation by factoring. (2x-13)^2 = 8

 

3) Find the domain of the expression. √x^2 - 36 (the whole thing is under the square root symbol)

Answer 1

1)

32=16*2

98=49*2

√32=√16*√2 = 4*√2

√98=√49*√2 = 7*√2

√32+√98 = 4√2 + 7√2 = (4+7)√2 = 11√2

 

2)

(2x-13)² = 8

2x-13= √8 = √4√2 = 2√2

2x=2√2+13

x=√2+13/2

 

3)

The domain is all of the x-values that provide real answers for your expression.

In order for this expression to provide real answers, the term that is being square rooted must be positive or zero.

x² - 36 ≥ 0

x² ≥ 36

|x| ≥ 6

So, either x ≥ 6 or x ≤ -6

So the domain of this function is all real numbers except those between (-6,6).