Math, please explain this.

[Shotline]

(sqrt(2))^3 = 2(sqrt(2))

Can someone please explain how the square root of 2 cubed equals 2 times the square root of 2?

Or point me to a web site that explains it?

Thanks much.

 

[JesasaurusRex]

e=mc2

 

[Papi-C]

The trick to this is that you're multiplying by 2

 

[2+2=5]

think of it like this

sqrt(2)^3 = sqrt(2)*sqrt(2)^2 = 2sqrt(2)

 

[Shotline]

think of it like this

sqrt(2)^3 = sqrt(2)*sqrt(2)^2 = 2sqrt(2)

sqrt(2)*sqrt(2) = 2, 2^2=4 doesn't it?

I know that sqrt(2) = 2^1/2 so how does (2^1/2)^3 = 2sqrt(2) ?

Unless I am mistaken, the powers rules say that (2^1/2)^3 should be 2^1/2(3) (two to the one half times three) which would be 2^3/2 which would be the cube root of the two squared (or is it the square root of two cubed), or do I have this all wrong?

 

[gnahc79]

(sqrt(2))^3 = 2(sqrt(2))

Can someone please explain how the square root of 2 cubed equals 2 times the square root of 2?

Or point me to a web site that explains it?

Thanks much.

http://www.themathpage.com/alg/multiply-radicals.htm
(sqrt(2))^3 = sqrt(2) * sqrt(2) * sqrt(2)
= sqrt(4) * sqrt(2)
= 2 * sqrt(2)

 

[UDRider]

sqrt(2)*sqrt(2) = 2, 2^2=4 doesn't it?

I know that sqrt(2) = 2^1/2 so how does (2^1/2)^3 = 2sqrt(2) ?

(2^.5)*(2^.5) = 2^1 you add .5s together.

 

[Ducky_Fresh]

(sqrt(2))^3 = 2(sqrt(2))

Can someone please explain how the square root of 2 cubed equals 2 times the square root of 2?

Or point me to a web site that explains it?

Thanks much.

1.4142135623730950488^3 = 2 x 1.4142135623730950488


Yep, works. 2.848...

 

[Climber]

Consider for a moment that sqrt(3)^3 = 3*sqrt(3)

 

[Ducky_Fresh]

1.4142135623730950488^3 = 2 x 1.4142135623730950488


Yep, works. 2.848...

Or rather:

2.848 = 2.848

 

[Shotline]

http://www.themathpage.com/alg/multiply-radicals.htm
(sqrt(2))^3 = sqrt(2) * sqrt(2) * sqrt(2)
= sqrt(4) * sqrt(2)
= 2 * sqrt(2)

Ok, this I can follow and it makes sense. But isn't there a rule that gets you there quicker?

 

[MrIncredible]

Ok, this I can follow and it makes sense. But isn't there a rule that gets you there quicker?

Probably, but it's moot. Long as you can prove it, you're right.

Unless it's a test on rules.

 

[Shotline]

Probably, but it's moot. Long as you can prove it, you're right.

Unless it's a test on rules.

No, the problem is:

Find the point(s) on the graph where the slope is equal to 3/2.

The graph is y=x^3

 

[gnahc79]

Ok, this I can follow and it makes sense. But isn't there a rule that gets you there quicker?

+1 on probably, but dear azn mom berated me for not showing all my work back in the day, I'm not physically able to do shortcuts anymore :laughing.

 

[UDRider]

sqrt(2)*sqrt(2) = 2, 2^2=4 doesn't it?

I know that sqrt(2) = 2^1/2 so how does (2^1/2)^3 = 2sqrt(2) ?

Unless I am mistaken, the powers rules say that (2^1/2)^3 should be 2^1/2(3) (two to the one half times three) which would be 2^3/2 which would be the cube root of the two squared (or is it the square root of two cubed), or do I have this all wrong?

Ok, this I can follow and it makes sense. But isn't there a rule that gets you there quicker?

When multiplying two numbers with an exponent, if the base is the same, exponents get added.

 

[2+2=5]

Ok, this I can follow and it makes sense. But isn't there a rule that gets you there quicker?

exponent rules

x^a * x^c = x^(a+c)

(x^a)^c = X^(ac)

[x^(1/2)]^3 = x^(3/2) = X^(1/2) * x^(1/2) * x^(1/2) = x^(1/2) * x^1

 

[Cycle61]

 

[Shotline]

exponent rules

x^a * x^c = x^(a+c)

(x^a)^c = X^(ac)

[x^(1/2)]^3 = x^(3/2) = X^(1/2) * x^(1/2) * x^(1/2) = x^(1/2) * x^1

Ya, I follow it all right. Just seems there would be a rule or something where you didn't have to write it out like that. Guess you just have to do it in your head or write it all out. Usually things in math seem so elegant, this seems a bit clumsy though.

 

[greener]

No, the problem is:

Find the point(s) on the graph where the slope is equal to 3/2.

The graph is y=x^3

What level math is permitted?
If Calculus is permitted, set the first derivative to 3/2?

3x² = 3/2

x² = (3/2)/3

x² = 2

x = √2 = ±1.414

 

[UDRider]

The problem can be solved by a recursive application of divide and conquer algorithm, while applying the exponent rule to the end of recursion. Seems elegant.