Log in Simone 11 years agoPosted 11 years ago. Direct link to Simone's post “does that mean that the I...” does that mean that the I can't simplify the cube root of 3? • (17 votes) Jayant Wakode 11 years agoPosted 11 years ago. Direct link to Jayant Wakode's post “we can not simplify cube ...” we can not simplify cube root 3...but..we can find its value by method of logaritms (2 votes) jasonsanctis 12 years agoPosted 12 years ago. Direct link to jasonsanctis's post “(3^3) X ( b^3) X (c^3) = ...” (3^3) X ( b^3) X (c^3) = (3bc)^ 3 • (6 votes) Matthew Daly 12 years agoPosted 12 years ago. Direct link to Matthew Daly's post “There's a separate rule t...” There's a separate rule that (a^m) * (b^m) = (ab)^m. If you think about it, it all comes down to basic principles. a^m is just m copies of a multiplied together, right? So a^m b^m is just a*a*...a*b*b...b, with n copies of each, so we can rearrange those terms using the commutative property to get that it is also a*b*a*b...*a*b, which is n copies of ab multiplied together or (ab)^n. (13 votes) tyrece14 10 years agoPosted 10 years ago. Direct link to tyrece14's post “i dont get how letters ca...” i dont get how letters can be perfect or not perfect • (3 votes) Anthony Jacquez 10 years agoPosted 10 years ago. Direct link to Anthony Jacquez's post “Perfect numbers just mean...” Perfect numbers just mean it has a square root that is a whole number. Non perfect numbers have a square root has is not a whole number and has decimals. (17 votes) Marina Burandt 11 years agoPosted 11 years ago. Direct link to Marina Burandt's post “What about bigger roots, ...” What about bigger roots, like root 4? A problem in my book is: simplify ^4 of z^8. What would I do there? • (5 votes) mahansen42 11 years agoPosted 11 years ago. Direct link to mahansen42's post “Roots can be turned into ...” Roots can be turned into fractional exponents. the n'th root can be re-written as an exponent of 1/n. So the 4th root of x is the same as x^(1/4). Once you get that, then you should be able to use properties of exponents to finish the problem. (5 votes) Pedro 11 years agoPosted 11 years ago. Direct link to Pedro's post “Hi! I would like to kno...” Hi! I would like to know why the cube root of a given number is equal to that same number to the power of 1/3, ³√x = x to the 1/3 power. Why 1/3? What makes it 1/3? That's something I'm having a little trouble understanding! Thanks in advance! Cheers! • (3 votes) Andrew M 11 years agoPosted 11 years ago. Direct link to Andrew M's post “That's a good question. ...” That's a good question. Take a look at this: We know that when you multiply numbers that have exponents, you add the exponents, right? So for example, 2^3 * 2^2 = 2^5. And likewise, 2^1 * 2^1 *2^1 = 2^3, which equals 8. Now let's try it with a variable for the exponent, where we are trying to find the cube root of 8 by raising 8 to some undetermined power: 8^x * 8^x * 8^x = 8^1 = 8. What does x have to be? When I add up three x's, I have to get 1. 3x =1. x = 1/3. So 8^(1/3) is the cube root of 8. You can show the same thing using the rule that says (a^n)^m = a^(n*m) (8^(1/3))^3 = 8^(1/3*3) = 8^1. (7 votes) imad ali 11 years agoPosted 11 years ago. Direct link to imad ali's post “what about taking the abs...” what about taking the absolute value here , is it not necessary in case of cube root? • (2 votes) HumXD 11 years agoPosted 11 years ago. Direct link to HumXD's post “i'm guessing you meant 'd...” i'm guessing you meant 'do we have to do like square root and take the positive root?' cube root is pretty much the opposite of taking the number to the power of 3 so... -2^3 = -2*-2*-2 = -8 if you get cuberoot(8), you have only 1 answer. (5 votes) Sophie 10 years agoPosted 10 years ago. Direct link to Sophie's post “What if the constant was ...” What if the constant was not a perfect cube? Like the number 24? How would you do that? Thanks • (3 votes) Trey Branch 9 years agoPosted 9 years ago. Direct link to Trey Branch's post “Is there any other way to...” Is there any other way to get the right answer?? • (3 votes) Stefen 9 years agoPosted 9 years ago. Direct link to Stefen's post “This is the process and S...” This is the process and Sal demonstrated it in excruciating detail. As you get used to the procedure, most of it you will be able to do in your head. (3 votes) Tom 10 years agoPosted 10 years ago. Direct link to Tom's post “Okay, I get this. Now wha...” Okay, I get this. Now what to do with the cube root of 9+4√5? According to wolfram and my calc it can be simplified to (3+√5)/2. I get the simplification steps wolfram offers, but I couldn't find the general way to simplify this kind of expressions. (Some other examples are the cube root of 40+11√13 which is (5+√13)/2, and the cube root of 10-6√3, which is 1-√3..) • (3 votes) Sainfroy, Ralph 7 years agoPosted 7 years ago. Direct link to Sainfroy, Ralph's post “thank you, cause khan aca...” thank you, cause khan academy and my teacher make me get everything happen in my class . love your (1 vote) Alex Wood 5 years agoPosted 5 years ago. Direct link to Alex Wood's post “At 3:06, Sal writes a 2 n...” At • (2 votes) Kim Seidel 5 years agoPosted 5 years ago. Direct link to Kim Seidel's post “If you watch closely, you...” If you watch closely, you will see he does write a 3, not a 2. (2 votes)Want to join the conversation?
say y=cube root3...taking log on both sides, log y =log(cuberoot 3)=(1/3)(log 3)
=(1/3)*0.48=0.16....now, log y =0.16....now we take antilog on both sides,,,,
y=antilog 0.16 = 1.4454.....so, cuberoot 3=1.4454
which property of exponents is Sal referring to,
is it : (a^m)^n = (a)^ mn...
my memory has misplaced this property.....oh
Also please guide me to the video which Sal is referring to .. i intend to review it..
Example:
Perfect:4,9,16,25,36,49,64,81
Non Perfect:3,5,7,45,56,67,78
2^3= 8
cuberoot(8)=2
cuberoot(-8)= -2
Keep practicing!
3:06
Video transcript
We're asked to simplify thecube root of 27a squared times b to the fifth timesc to the third power. And the goal, wheneveryou try to just simplify a cube root likethis, is we want to look at the parts ofthis expression over here that are perfect cubes,that are something raised to the third power. Then we can take justthe cube root of those, essentially taking themout of the radical sign, and then leavingeverything else that is not a perfectcube inside of it. So let's see what we can do. So first of all, 27--you may or may not already recognize thisas a perfect cube. If you don't alreadyrecognize it, you can actually doa prime factorization and see it's a perfect cube. 27 is 3 times 9,and 9 is 3 times 3. So 27-- its prime factorizationis 3 times 3 times 3. So it's the exact same thingas 3 to the third power. So let's rewrite thiswhole expression down here. But let's write it in terms ofthings that are perfect cubes and things that aren't. So 27 can be just rewrittenas 3 to the third power. Then you have a squared--clearly not a perfect cube. a to the third would have been. So we're just goingto write this-- let me write it over here. We can switch the orderhere because we just have a bunch of things beingmultiplied by each other. So I'll write the asquared over here. b to the fifth is not aperfect cube by itself, but it can be expressedas the product of a perfect cube andanother thing. b to the fifth is the exact same thing asb to the third power times b to the second power. If you want to see thatexplicitly, b to the fifth is b times b timesb times b times b. So the first three areclearly b to the third power. And then you have b tothe second power after it. So we can rewrite b tothe fifth as the product of a perfect cube. So I'll write bto the third-- let me do that in thatsame purple color. So we have b to thethird power over here. And then it's b to thethird times b squared. So I'll write the bsquared over here. And we're assuming we're goingto multiply all of this stuff. And then finally, wehave-- I'll do in blue-- c to the third power. Clearly, this is a perfect cube. It is c cubed. It is c to the third power. So I'll put it over here. So this is c to the third power. And of course, we still havethat overarching radical sign. So we're still trying to takethe cube root of all of this. And we know from ourexponent properties, or we could say fromour radical properties, that this is theexact same thing. That taking the cube rootof all of these things is the same astaking the cube root of these individual factorsand then multiplying them. So this is the samething as the cube root-- and I could separatethem out individually. Or I could say the cuberoot of 3 to the third b to the third c to the third. Actually, let's do it both ways. So I'll take themout separately. So this is the same thingas the cube root of 3 to the third times the cuberoot-- I'll write them all in. Let me color-code it so we don'tget confused-- times the cube root of b to the thirdtimes the cube root of c to the third timesthe cube root-- and I'll just groupthese two guys together just because we're notgoing to be able to simplify it any more-- times the cuberoot of a squared b squared. I'll keep the colorsconsistent while we're trying to figureout what's what. And I could have said thatthis is times the cube root of a squared timesthe cube root of b squared, but that won'tsimplify anything, so I'll just leavethese like this. And so we can look atthese individually. The cube root of 3 to thethird, or the cube root of 27-- well, that's clearlyjust going to be-- I want to do that inthat yellow color-- this is clearlyjust going to be 3. 3 to the third power is3 to the third power, or it's equal to 27. This term right overhere, the cube root of b to the third--well, that's just b. And the cube rootof c to the third, well, that isclearly-- I want to do that in that-- thatis clearly just c. So our whole expression hassimplified to 3 times b times c times the cube rootof a squared b squared. And we're done. And I just want todo one other thing, just because I did mentionthat I would do it. We could simplify it this way. Or we could recognize thatthis expression right over here can be written as 3bcto the third power. And if I take threethings to the third power, and I'm multiplying it,that's the same thing as multiplying themfirst and then raising to the third power. It comes straight out ofour exponent properties. And so we can rewritethis as the cube root of all of this timesthe cube root of a squared b squared. And so the cuberoot of all of this, of 3bc to the third power, well,that's just going to be 3bc, and then multiplied by the cuberoot of a squared b squared. I didn't take the troubleto color-code it this time, because we already figuredout one way to solve it. But hopefully, thatalso makes sense. We could have donethis either way. But the important thing isthat we get that same answer.
