SOLUTION: Without using a calculator, tell which is larger: the positive 6th root of 10 or the 3rd root of 3?

Question 23256: Without using a calculator, tell which is larger: the positive 6th root of 10 or the 3rd root of 3?
Found 2 solutions by stanbon, rapaljer:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Raise both to the 6th power:
[6th root of 10}^6 = 10
[3rd root of 3]^6 = 3^2=9
So, 6th root is larger
Cheers,
Stan H.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
It is worth mentioning that the solution presented here by tutor Stanbon is valid ASSUMING that the numbers being raised to the 6th power (i.e., and ) are greater than 1! This argument does NOT work for values of x where .

Excellent solution! Hats off to Stanbon!!

R^2 at SCC
RELATED QUESTIONS
Evalute the expression without using a calculator. log10 cube root of... (answered by Alan3354)
how do we tell, without using the calculator to find explicitly, whether a square root,... (answered by asuar010)
Find the degree measure of θ, without using a calculator. θ= arccos (square... (answered by lwsshak3)
Without using a calculator, list the numbers square root of 2, cube root of 3, and fifth... (answered by venugopalramana)
For positive real numbers x, y, and z,which of the following expressions is equivalent to (answered by stanbon)
Without using a calculator or computer, determine which is larger, 2^3000 or... (answered by richwmiller,CharlesG2)
Please help me solve this problem. Which is larger: 3rd root of 1/4 or the 4th... (answered by checkley77)
Evaluate the expression without using a calculator log9 1/sq root of... (answered by stanbon)
Without using a calculator which is larger: x= 7^1/4 or y=4^1/3 (answered by Edwin McCravy)