+16 The square root of a positive number is twice as big as the cube of that number. What is the number?
+129840 Let N be the number...so we have
N^(1/2) = 2N^3 rearrange as
2N^3 - N^(1/2) = 0 factor
N^(1/2) (2N^(2.5) - 1) = 0 set each factor to 0
N^(1/2) = 0 → N = 0 [ reject.....0 isn't positive...]
And
2N^(2.5) - 1 = 0 rearrange
2 N^(2.5) = 1 divide by 2
N^(2.5) = 1/2 → N = (1/2)^(1/2.5) = (.5)^(0.4) ≈ .75786
CPhill: I read the question differently!
sqrt(x) = 2(x)^(1/3), solve for x
Solve for x:
sqrt(x) = 2 x^(1/3)
Raise both sides to the 6 power:
x^3 = 64 x^2
Subtract 64 x^2 from both sides:
x^3 - 64 x^2 = 0
Factor x^2 from the left hand side:
x^2 (x - 64) = 0
Split into two equations:
x - 64 = 0 or x^2 = 0
Add 64 to both sides:
x = 64 or x^2 = 0
Take the square root of both sides:
Answer: |x = 64 [ or x = 0] discard this one.
