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  2. What is the square root of zero? - Socratic

    socratic.org/questions/what-is-the-square-root-of-zero

    1 Answer. The √0 will be equal to 0 because 02 = 0. Think of √0 meaning the square root of 0 objects, if you have no objects to square root, then the answer will be 0. The sqrt0=0 The sqrt0 will be equal to 0 because 0^2=0.

  3. What is the square root of 256? - Socratic

    socratic.org/questions/what-is-the-square-root-of-256

    1 Answer. George C. May 30, 2015. √256 = 16. at least that's the positive square root. −16 is also a square root of 256. 162 = (−16)2 = 256. By definition, the principal square root of a number is the positive square root. The term "the square root" is commonly used to refer to the principal (positive) root though there are usually two roots.

  4. What is the square root of negative one? + Example - Socratic

    socratic.org/questions/what-is-the-square-root-of-negative-one

    The principal square root of minus one is i. It has another square root -i. I really dislike the expression "the square root of minus one". Like all non-zero numbers, -1 has two square roots, which we call i and -i. If x is a Real number then x^2 >= 0, so we need to look beyond the Real numbers to find a square root of -1. Complex numbers can be thought of as an extension of Real numbers from ...

  5. Square Root - Prealgebra - Socratic

    socratic.org/prealgebra/exponents-radicals-and-scientific-notation/square-root

    How do you simplify 36/sqrt15? A checkerboard has an area of 576 cm Each side of the board is made of 8 small squares. What is the side length of each small square on the board? While finding root of a square number why we take pairs of number from right, but not left? What is sqrt ( (x-1)^2)? Simplify 2sqrt27+3sqrt12?

  6. Why does sqrtx=x^(1/2)? + Example - Socratic

    socratic.org/questions/why-is-the-square-root-of-x-x-1-2

    The reason this is true is that fractional exponents are defined that way. For example, x^(1/2) means the square root of x, and x^(1/3) means the cube root of x. In general, x^(1/n) means the nth root of x, written root(n)(x).

  7. What is the square root of 1/2? - Socratic

    socratic.org/questions/what-is-the-square-root-of-1-2

    Help. See a solution process below: Square root of 1/2 = sqrt (1/2) We can use this rule for radicals to rewrite the expression: sqrt (color (red) (a)/color (blue) (b)) = sqrt (color (red) (a))/sqrt (color (blue) (b)) sqrt (color (red) (1)/color (blue) (2)) => sqrt (color (red) (1))/sqrt (color (blue) (2)) => 1/sqrt (2) Now, we can rationalize ...

  8. What is the square root of x squared? - Socratic

    socratic.org/questions/what-is-the-square-root-of-x-squared

    The term 'the square root of X' is not quite precise as there are usually 2 square roots called sqrt(X) and -sqrt(X) sqrt(x^2) = abs(x) This is the positive square root of x^2. -sqrt(x^2) = -abs(x) is also a square root of x^2 It's tempting to say sqrt(x^2) = x, but that's only true for x>=0

  9. What is the square root of -2? - Socratic

    socratic.org/questions/what-is-the-square-root-of-2

    The square root symbol means the one without a minus sign in front, so √−2 = √2i or i√2. The answer your teacher will give depends on where you are in you mathematics education. There is no positive or negative number that is the square root of -2 If we square a positive number we get a positive answer. If we square a negative number ...

  10. What is the square root of 89? - Socratic

    socratic.org/questions/what-is-the-square-root-of-89

    The square root of 89 is a number which when squared gives 89. sqrt(89) ~~ 9.434 Since 89 is prime, sqrt(89) cannot be simplified. You can approximate it using a Newton Raphson method. I like to reformulate it a little as follows: Let n = 89 be the number you want the square root of. Choose p_0 = 19, q_0 = 2 so that p_0/q_0 is a reasonable rational approximation. I chose these particular ...

  11. Why are square roots irrational? + Example - Socratic

    socratic.org/questions/why-are-square-roots-irrational

    So, if a square root is not a perfect square, it is an irrational number. First, not all square roots are irrational. For example, sqrt (9) has the perfectly rational solution of 3 Before we go on, let's review what it means to have an irrational number - it has to be a value that goes on forever in decimal form and is not a pattern, like pi.