what is the cube root of 1000

³√1000 is 10. i.e. 10 × 10 × 10 = 1000.

10

10

The cube root of 1000 (one thousand) equals exactly 10. There is no other number that when, multiplied by itself twice, will equal 1000.

10 times 10 times 10 = 1000.0000
9.9999 times 9.9999 times 9.9999 = 999.9700
10.0001 times 10.0001 times 10.0001 = 1000.0300

The cube root of 1000 (or any other number) can be designated by using the radical sign (modified capital letter V with shortened leg on the left leg of the V and a horizontal line sufficiently long to accommodate the number extending to the right), inserting the number 1000 (or other) under the line (in the box so to speak) and placing a small 3 (to designate cube root) within the notch of the V. A V-notch without a number is understood to designate square root, a V-notch with a number 4 designates the fourth root, etc.

For Yahoo! Answers, it is best to designate the cube root of a number x as x^1/3 (square root would be designated as x^1/2 and other roots designated as ^1/4 for fourth root, ^1/5 for fifth root, etc.).

We all know that it is much easier to draw this radical and its associated numbers than it is to describe how to do it!

You are really asking us to solve the equation

x^3 - 1000 = 0

Clearly 10 is a cube root. So factorising the left hand side we get:

(x - 10) (x^2 + 10x + 100) = 0

We can factorise the second factor here by 'completing the square', the standard way of solving quadratic equations. We get

(x + 5)^2 + 75 = 0 and therefore

(x + 5)^2 = -75

No square of a real number can be negative, but if we introduce complex numbers where 'i' is defined to be the square roote of -1, we can proceed to solve the equation. We can write -75 as (sqrt(75)i)^2. Thus

(x + 5)^2 = (sqrt(75)i)^2

Taking the square root of each side and introducing plus or minus on the right hand side (since (-z)^2 = (z)^2 for all complex z),

x + 5 = sqrt(75)i or -sqrt(75)i or

x + 5 = 5 sqrt(3) i or -5 sqrt(3) i giving

x = -5 (1 + sqrt(3)i) or -5 (1 - sqrt(3)i)

which gives the final two solutions. We thus have three solutions to your question which is the maximum has a cubic polynomial can have at most three roots.

Cube Root Of 1000

³√1000
= ³√(10 x 10 x 10)
= 10

10 since 10^3=1000

10

10 x 10 x 10 = 1000

The answer is 10.

1000 = 10*10*10

Therefore, root 1000 = 10

cube root of 1000 is 10