A worked example of simplifying the cube root of 27a²b⁵c³ using the properties of exponents. A worked example of simplifying the cube root of 27a²b⁵c³ using the properties of exponents. If you're seeing this message, it means we're having trouble loading external resources on our website.
Learn how to simplify cube roots in this video. To see all my math videos, check out my channel at http://YouTube.com/MathMeeting.
Simplifying Radical Expressions1. Simplifying Radical Expressions1. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
This page will help you to simplify a term under a radical sign. Type your term under the radical sign. The little box to the upper left of the radical sign is the power of the radical. Putting a 2 here means square root. Putting a 3 here means cube root, etc.
The terms in this expression are both cube roots, but I can combine them only if they're the cube roots of the same value. Right now, they aren't. So I'll simplify the radicals first, and then see if I can go any further. I note that 8 = 2 3 and 64 = 4 3, so I will actually be able to simplify the radicals completely.
If you need a refresher on simplifying radicals with numerical values, see the Refresher section, Simplifying Radicals. In this section, we will concentrate on examining algebraic cube roots and higher-index roots.
Students learn to simplify a square root by setting up a factor tree for the number inside the radical. If a factor pairs up in the factor tree, then it comes out of the radical. If a factor does not pair up, then it stays inside. Students also learn to simplify a cube root by setting up a factor tree for the number inside the radical.
To simplify radicals, rather than looking for perfect squares or perfect cubes within a number or a variable the way it is shown in most books, I choose to do the problems a different way, and here is how. Here are the steps required for Simplifying Radicals:
Simplifying Radicals Date_____ Period____ Simplify. Use absolute value signs when necessary. 1) 24 2 6 2) 3 1000 10 3) 3 −162 −3 3 6 4) 512 16 2 5) 4 128 n8 2n2 4 8 6) 98 k 7 2k 7) 5 224 r7 2r 5 7r2 8) 3 24 m3 2m 3 3 9) 392 x2 14 x 2 10) 512 x2 16 x 2 11) 4 405 x3y2 3 4 5x3y2 12) 3 −16 a3b8 −2ab2 3 2b2 13) 4 128 x7y7 2 x ⋅ y 4 8x3y3 ...
In this video we look at an example of simplifying a cubic root that has variables as well as a number in the radicand.