Higher order roots

If you practiced with square roots before, you'll figure out how this works. What is the volume of this cube? The volume of a cube is the length of the side times the side times the side. In other words, the side to the power of three - 3 times 3 times 3 equals 27 cubic centimeters if the side is 3 centimeters. 27 cubic meters if the side is 3 meters.

Here's another cube. It has a volume of 64, how long is the side? In other words, which number multiplied by itself 3 times equals 64? To find out, we use the square root's scary sister, the cube root. It's not that complicated.

It looks like the square root, but with one difference. Look above the small 'v'. You can see number three there. That is the root's degree. In this case, three which means a cube root.

The number you are taking the root of is called the "radicand," but the word is not used often. This problem says, which number raised to the power of 3 equals 64? When the root sign is without a number then the degree is two then it always means a square root. There exists roots of other degrees than square and cube. If you change the degrees to 4 like this, you read it as the fourth root of 256.

Only the degrees two and three have their special names, square and cube. After that, they are called the fifth, sixth, and seventh root of a number. The degree above the root sign is equivalent to the power in an exponential expression. The fourth root of 256 is 4 since 4 to the power of 4 is 256. Or more generally, the nth root of y is y.

If Y to the power of n is x. Roots are similar to exponential expressions but inverse - n is the degree, a is the radicand. Find the number that if raised to the power of n equals a. If the nth root of a is x, then x to the power of n equals a.