Skip to main content
  1. Life
  2. Education & Schools
  3. General Education

Simplying radical expressions with variables

See also

Sometimes we will say terms such as x^2 or x^3 under radical signs. What do we do in such a situation? If what we're dealing with is a radical with a square root, we try to raise it by an even power, whereas if it is a cubed root, we try to leave it as a power of three. For example, if we have something like the square root of x^4y^2, we come up with x^2y. If we have something like the square root of a^3, we find this by writing a^2 times a.

We then end up with one a to the left of the radical sign, and the other to the right. If we have something like x^5, we right x^4 times x, and then we leave the x under the square root sign, and we place x^2 to the left of the square root sign. If we have something like y^4, we also end up with y^2 to the left of the square root sign, but unlike x^5, we do not leave any y under the square root sign. One of the keys to the process involves removing as many perfect cubes from under the square root sign as possible. Use the multiplication described above to place perfect squares to the left of the square root symbol by simplying them under the square root sign with multiplication. This will involve leaving variables to the 1th power (without variables) under the square root symbol.

Advertisement