Cube root

[chrisheaven]

A number that must be multiplied times itself three times to equal a given number.
The cube root of 8 is 2

 

[chrisheaven]

A friend asked me to pick a number between 100 and 200, cube it, and give him the answer. After thinking about it, he gave me the original number that I had cubed--the cube root of the number I gave him. How does he do this in his head without a calculator?

 

[isabeau]

uh you are asking me????

 

[milagros317]

A friend asked me to pick a number between 100 and 200, cube it, and give him the answer. After thinking about it, he gave me the original number that I had cubed--the cube root of the number I gave him. How does he do this in his head without a calculator?

Some people, with the unflattering name of idiot savants, can do complex arithmetic calculations in their heads.

 

[chrisheaven]

could that be the only explanation?

 

[milagros317]

No. He could have memorized all the two-digit endings of perfect squares and know the last two digits of their possible square roots. Then he only needs a rough estimate to get the first digit and pick the second.

Example: A perfect square ending in 96 has a square root that ends in either 14, 36, 64 or 86.

So you tell him the square is 98,596 and he knows the square root is x14, x36, x64, or x86, where x is a digit from 1 to 9.

He then needs to estimate that the square root of 98,596 is over 300 (square 90,000) but under 320 (square 102,400), so the answer is 314.

 

[chrisheaven]

that would be a more likely option

 

[huskys]

No. He could have memorized all the two-digit endings of perfect squares and know the last two digits of their possible square roots. Then he only needs a rough estimate to get the first digit and pick the second.

Example: A perfect square ending in 96 has a square root that ends in either 14, 36, 64 or 86.

So you tell him the square is 98,596 and he knows the square root is x14, x36, x64, or x86, where x is a digit from 1 to 9.

He then needs to estimate that the square root of 98,596 is over 300 (square 90,000) but under 320 (square 102,400), so the answer is 314.

Of course ................ its as easy as that ................

 

[milagros317]

1 has only one real cube root but three complex cube roots. 😀

 

[chrisheaven]

what about the cube root of 3i?

 

[milagros317]

There are three of them, none real. 😀

 

[chrisheaven]

i imagined there would be

 

[milagros317]

All non-zero complex numbers have three distinct complex roots. 😀

 

[chrisheaven]

Ever been to Cuba, Mils?

 

[milagros317]

No, I've never been to Cuba. I passed quite close to it in a ship that docked in San Juan. 😀

 

[chrisheaven]

then you got close to the root of the matter eh?

 

[milagros317]

Have you ever been to Cuba? At least in your case, you could legally go there. 😀

 

[chrisheaven]

no--I would love to go there and see it-all those cub(an) roots on those trees

 

[milagros317]

I expect to visit there someday after Castro dies and the restrictiions are lifted. 😀

 

[chrisheaven]

what about Cubism?

 

[milagros317]

What about it? I like the work of Picasso and Braque. 😀

 

[chrisheaven]

here is a copy of a George braque lithograph

 

[milagros317]

The cube root of 1331 is 11. 😀

 

[chrisheaven]

what would the cube root of z be?

 

[milagros317]

That would depend on what z is. 😛

If z in polar form is actually r*e^(i*theta), then its three cube root are

r^(1/3) * e^(i*theta/3)

r^(1/3) * e^(i*(theta/3 + 2*pi/3)) and

r^(1/3) * e^(i*(theta/3 + 4*pi/3))