Taken from another post. How would you evaluate that fraction, or specifically (out of my homework) 4rt(81) [note that the 4 is the n). I got the bright idea that it might be rooted 4 times, but I get rt(3) and my math book says it's simply 3. Please explain.

2. Originally Posted by Harness

Taken from another post. How would you evaluate that fraction, or specifically (out of my homework) 4rt(81) [note that the 4 is the n). I got the bright idea that it might be rooted 4 times, but I get rt(3) and my math book says it's simply 3. Please explain.

Observe that $\displaystyle x = 81^{1/4} = (81^{1/2})^{1/2} = 9^{1/2} = 3$

So to find $\displaystyle x$, square root 81 twice, once to get 9 and a second time to get the answer: 3.

Raising a number to the one-fourth power does not mean that you are square rooting it four times. Instead, it is asking: which number multiplied by itself four times gets you the original number? In other words, which number multiplied by itself four times gets you 81? That number is defined as $\displaystyle 81^{1/4}$, or 3.

3. Originally Posted by Last_Singularity
Observe that $\displaystyle x = 81^{1/4} = (81^{1/2})^{1/2} = 9^{1/2} = 3$

So to find $\displaystyle x$, square root 81 twice, once to get 9 and a second time to get the answer: 3.

Raising a number to the one-fourth power does not mean that you are square rooting it four times. Instead, it is asking: which number multiplied by itself four times gets you the original number? In other words, which number multiplied by itself four times gets you 81? That number is defined as $\displaystyle 81^{1/4}$, or 3.
Okay, thanks, that makes sense to me