SOLUTION: Can someone please please help me with these questions. I am preparing for a quiz on Monday. 1) z sqrt 80zu^2 - u sqrt 5z^3 2) sqrt z +16 = sqrt 7z+12 3) sqrt -6w+16=w

Algebra ->  Square-cubic-other-roots -> SOLUTION: Can someone please please help me with these questions. I am preparing for a quiz on Monday. 1) z sqrt 80zu^2 - u sqrt 5z^3 2) sqrt z +16 = sqrt 7z+12 3) sqrt -6w+16=w       Log On


   

Question 228591: Can someone please please help me with these questions. I am preparing for a quiz on Monday.
1) z sqrt 80zu^2 - u sqrt 5z^3
2) sqrt z +16 = sqrt 7z+12
3) sqrt -6w+16=w
4) sqrt 10+8 / -5 sqrt 10+1
Thank you in advance
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1) z%2Asqrt%2880zu%5E2%29+-+u%2Asqrt%285z%5E3%29
Factor to reveal the perfect squares
z%2Asqrt%2816%2A5%2Az%2Au%5E2%29+-+u%2Asqrt%285%2Az%5E2%2Az%29
extract the squares and combine like terms
4uz%2Asqrt%285z%29+-+uz%2Asqrt%285z%29 = 3uz%2Asqrt%285z%29
;
;
2) sqrt%28z%2B16%29+=+sqrt%287z%2B12%29
Square both sides:
z + 16 = 7z + 12
16 - 12 = 7z - z
4 = 6z
z = 4%2F6 = 2%2F3
;
;
3) sqrt%28-6w%2B16%29+=+w
square both sides
-6w + 16 = w^2
0 = w^2 + 6w - 16
Factors to:
(w+8)(w-2) = 0
Two solutions
w = -8
w = +2;
Check both solutions in the original equation (only one is valid)
:
:
4) sqrt%2810%2B8%29%2F%28-5%2Asqrt%2810%2B1%29%29 = sqrt%2818%29%2F%28-5%2Asqrt%2811%29%29 = sqrt%289%2A2%29%2F%28-5%2Asqrt%2811%29%29 = -3%2Asqrt%282%29%2F%285%2Asqrt%2811%29%29