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How do you calculate the roots of numbers other than cubes or squares?
Wiki User
∙ 9y ago
One way to find such a root is iteration. This entails making a guess at the answer and then improving on it. Repeating the procedure should lead to a better estimate at each stage. One such is the Newton-Raphson method.
If you want to find the rth root of k, define f(x) = x^r – k. Then finding the rth root of k is equivalent to solving f(x) = 0.Let f’(x) = r*x^(r-1). This is the derivative of f(x) but you do not need to know that to use the N-R method.
Start with x(0) as the first guess.
Then let x(n+1) = x(n) - f[x(n)]/f’[(x(n)] for n = 0, 1, 2, … Provided you made a reasonable choice for the starting point, the iteration will very quickly converge to the true answer. It works even if your first guess is not so good. Suppose you want the 5th root of 10.
Suppose you start with x(0) = 2 (a pretty poor choice since 2^5 is 32, which is nowhere near 10).
Even so, x(4) = 1.5849, which is less than a quarter of one millionths from the true value.
Wiki User
∙ 9y ago
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What numbers are squares and cubes of other numbers?
All non-negative numbers (including zero) are real-number squares of other numbers.All numbers (positive, negative, and zero) are cubes of other numbers."Numbers" generally refers to the set of all real numbers. 2 is the square of a real number, √2. √2 is not a whole number. It's not even rational. But it is a real number, and therefore meets the criteria specified. Even pi (π), an irrational number itself, is the square of another real number (√π). The only real numbers that cannot be squares are negative numbers, because squares of negative numbers are always positive, because the product of two negative numbers is always positive. This restriction, however, does not apply to cubes, because if you multiply three negative numbers by each other, the result is negative.Now, for the question you may have meant to ask: "What numbers are squares and cubes of whole numbers (integers)?"It would be impossible to list all squares and cubes of integers, because even when you limit it to integers, there is still an infinite number of numbers, and every one of them has both a square and a cube.Examples of integers, their squares, and their cubes.0, 0, 01, 1, 1(-1, 1, -1)2, 4, 8,(-2, 4, -8)3, 9, 274, 16, 645, 25, 12510, 100, 1000Only a very few numbers, such as 0, 1, and 64, are both squares and cubes of integers. Note that 64 is 43 and also 82. (see the related question)
How do you calculation standard deviation of concrete cubes?
You cannot calculate standard deviation for objects such as concrete cubes - you can only calculate standard deviation for some measure - such as side length, surface area, volume, mass, alkalinity or some other measure.
How many numbers are there between the squares of 12 and 13?
Infinitely many. There are infinitely many numbers between any two numbers - no matter how close to each other they are.
Are numbers from 1 to 100 which numbers are perfect squares?
You can check which number from 1 to a 100 are squares of other numbers for yourself. Here's how: Start with 1 and count up, squaring the number and recording the result. Example: 12 = 1 22 = 4 32 = 9 . . . 102 = 100 The number 1, 3, 9 . . . 10 are squares Now, fill in the rest
Which of the sets of numbers is a Pythagorean Triple?
The one in which the square of the biggest one is equal to the sum of the squares of the other two is.
What numbers are squares and cubes of other numbers?
All non-negative numbers (including zero) are real-number squares of other numbers.All numbers (positive, negative, and zero) are cubes of other numbers."Numbers" generally refers to the set of all real numbers. 2 is the square of a real number, √2. √2 is not a whole number. It's not even rational. But it is a real number, and therefore meets the criteria specified. Even pi (π), an irrational number itself, is the square of another real number (√π). The only real numbers that cannot be squares are negative numbers, because squares of negative numbers are always positive, because the product of two negative numbers is always positive. This restriction, however, does not apply to cubes, because if you multiply three negative numbers by each other, the result is negative.Now, for the question you may have meant to ask: "What numbers are squares and cubes of whole numbers (integers)?"It would be impossible to list all squares and cubes of integers, because even when you limit it to integers, there is still an infinite number of numbers, and every one of them has both a square and a cube.Examples of integers, their squares, and their cubes.0, 0, 01, 1, 1(-1, 1, -1)2, 4, 8,(-2, 4, -8)3, 9, 274, 16, 645, 25, 12510, 100, 1000Only a very few numbers, such as 0, 1, and 64, are both squares and cubes of integers. Note that 64 is 43 and also 82. (see the related question)
Why it is important to sequence the content of curriculum?
There are some things that can be taught and understood only after other things. For example, square roots and cube roots will make sense only after you know about squares and cubes. Furthermore, squares and cubes will only make sense if you know about multiplication.
How do you calculation standard deviation of concrete cubes?
You cannot calculate standard deviation for objects such as concrete cubes - you can only calculate standard deviation for some measure - such as side length, surface area, volume, mass, alkalinity or some other measure.
Calculate the length of the hypotenuse?
The length of the hypotenuse is equal to the root of the sum of the squares of the other two sides.
The sum of two numbers is 24 find the numbers whose squares are to be minimum?
12 and 12, whose squares will be 144 each. If either of the numbers is smaller than 12, then the other will be larger than 12 and its square will be larger than 144.
How many numbers are there between the squares of 12 and 13?
Infinitely many. There are infinitely many numbers between any two numbers - no matter how close to each other they are.
What are numbers called that have square roots but are not a square number?
There is no specific name but they comprise the set of non-negative numbers other than perfect squares.
How are rubik's cubes made?
They are made by other cubes .
Are numbers from 1 to 100 which numbers are perfect squares?
You can check which number from 1 to a 100 are squares of other numbers for yourself. Here's how: Start with 1 and count up, squaring the number and recording the result. Example: 12 = 1 22 = 4 32 = 9 . . . 102 = 100 The number 1, 3, 9 . . . 10 are squares Now, fill in the rest
How do you calculate 66013.42 to get a number 66087?
You cannot.66013.42 and 66087 are two entirely different numbers. You cannot "calculate" one to the other.You cannot.66013.42 and 66087 are two entirely different numbers. You cannot "calculate" one to the other.You cannot.66013.42 and 66087 are two entirely different numbers. You cannot "calculate" one to the other.You cannot.66013.42 and 66087 are two entirely different numbers. You cannot "calculate" one to the other.
Which of the sets of numbers is a Pythagorean Triple?
The one in which the square of the biggest one is equal to the sum of the squares of the other two is.
Is the cubes root of negative 125 rational?
One of them is: -5 = -5/1 The other two cube roots are complex numbers.
