SOLUTION: 1) Solve the following equations. sqrt x-1=3 a) Answer: Show work in this space. b) sqrt x^3=8 . Answer: Show work in this space. c) 3 sqrt x^2=

Algebra ->  Square-cubic-other-roots -> SOLUTION: 1) Solve the following equations. sqrt x-1=3 a) Answer: Show work in this space. b) sqrt x^3=8 . Answer: Show work in this space. c) 3 sqrt x^2=      Log On


   

Question 73009: 1) Solve the following equations. sqrt x-1=3
a)
Answer:
Show work in this space.



b) sqrt x^3=8 .
Answer:
Show work in this space.



c) 3 sqrt x^2=4 .
Answer:
Show work in this space.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
sqrt%28x-1%29=3 I'm assuming it looks like this
%28sqrt%28x-1%29%29%5E2=%283%29%5E2Square both sides, this undoes the square root.
x-1=9Solve for x
x=10
Check:
sqrt%2810-1%29=3
sqrt%289%29=3
3=3Works


b)
sqrt%28x%5E3%29=8
%28sqrt%28x%5E3%29%29%5E2=8%5E2Square both sides
x%5E3=64
3%2Asqrt%28x%5E3%29=3%2Asqrt%2864%29Take cube root of both sides. Note: 3%2Asqrt%28x%29 is the cube root of x
x=4
Check:
sqrt%284%5E3%29=8
sqrt%2864%29=8
8=8Works


c)
3%2Asqrt%28x%5E2%29=4
sqrt%28x%5E2%29=4%2F3Divide by 3
%28sqrt%28x%5E2%29%29%5E2=%284%2F3%29%5E2Square both sides
x%5E2=16%2F9Simplify the right side
x=4%2F3Take the square root of both sides and solve
Check:
3%2Asqrt%28%284%2F3%29%5E2%29=4
3%2Asqrt%2816%2F9%29=4
3%2A%284%2F3%29=4
4=4Works
Hope that helps.