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What is the cube root of 400?

Updated: 12/5/2022
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Q: What is the cube root of 400?
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What is a number that you can cube to give an answer bigger than 200 but smaller than 400?

There are two integer answers : 6 and 7. Any value between 5.848 (cube root of 200) and 7.368 (cube root of 400) will satisfy the question.


How do you find the smallest positive integer of a variable in a cube root so that the cube root is an integer ex. find the smallest positive integer g so that the cube root of 400g is an integer?

Here is a method: cube root of 400g = n, where n is an integer cube both sides: 400g = n3 then: g = n3/400 therefore: n3/400 must be an integer if this is so, then n3 must be divisible by 400 with no remainder, and n must be => cube root of 400 which is 7.368 bracket the answer by substitution: let n=8, n cubed = 512 no good let n=12, n cubed = 1728 no good let n=20, n cubed = 8000, 8000/400=20 OK No smaller value of n will be divisible by 400 without a remainder, so g=20 is the smallest positive integer that meets the requirement.


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There is no such thing as a cube route. The cube root of -3 is -1.4422 (approx).There is no such thing as a cube route. The cube root of -3 is -1.4422 (approx).There is no such thing as a cube route. The cube root of -3 is -1.4422 (approx).There is no such thing as a cube route. The cube root of -3 is -1.4422 (approx).


What is equal to the square root of 20?

4.4721359549995793928183473374626 and -4.4721359549995793928183473374626 The cube root of 400 is also equal to the square root of 20. (IIRC) Another way to approach it: √(20)=√(4x5) =2√(5)