Solving Radical ExpressionsDate: 07/26/98 at 14:03:05 From: sherri Subject: Radical expressions I am having problems solving radical expressions. For example, how do you solve the cube root of 32 minus the cube root of 108? What about 2 times the cube root of 125 minus 5 times the cube root of 64? Please help! Date: 07/26/98 at 16:49:02 From: Doctor Ken Subject: Re: Radical expressions Hi Sherri, In these problems, let's think about what "cube root" means. The cube root of X is a number you can multiply by itself 3 times to get X. So the cube root of 8 is 2, since you can multiply 2*2*2 to get 8. Now let's learn a couple of things about cube roots. To make writing easier here, I'll use {X} to mean the cube root of X, {8} to mean the cube root of 8, and so on. Let's say we have the cube root of 72, {72}. We can change this some to make it perhaps easier to deal with. Since 72 = 2*2*2*3*3, we can rewrite {72}: {72} = {2*2*2*3*3} = {2*2*2}*{3*3} = 2*{9} When you're trying to pull numbers out of cube roots, you should look for these groups of 3 of the same numbers. I factored 72, and noticed that there were three 2's in it. So I could pull those out of the cube root. Now let's try your problems. Your first problem is {32} - {108}. Let's factor them: {32} - {108} = {2*2*2*2*2} - {2*2*3*3*3} (factor) = {2*2*2*2*2} - {3*3*3*2*2} (change the order) = {2*2*2}*{2*2} - {3*3*3}*{2*2} (separate) = 2*{2*2} - 3*{2*2} (take cube root of 8 and 27) = (2-3)*{2*2} (factor out {2*2}) = -1*{4} (simplify the parts) = -{4} (simplify) So the cube root of 32 minus the cube root of 108 is equal to the negative of the cube root of 4. In your next problem, you have 2*{125} - 5*{64}. I'll get you started: 2*{125} - 5*{64} = 2*{5*5*5} - 5*{2*2*2*2*2*2} = ... Notice that you could also make {64} into {4*4*4} if you wanted to. Good luck! - Doctor Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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