what is the square root of 2 times 12?

4.9 (rounded)

In mathematics, a square root of a number x is a number r such that r^2=x, or in words, a number r whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root and denoted with a radical symbol as sqrt x. For example, the principal square root of 9 is 3, denoted sqrt 9 = 3, because 3^2 = 3times3 = 9. The other square root of 9 is −3.

Square roots often arise when solving quadratic equations, or equations of the form ax^2+bx+c=0, due to the variable x being squared.

Every positive number x has two square roots. One of them is sqrt{x}, which is positive, and the other is -sqrt{x}, which is negative. Together, these two roots are denoted pmsqrt{x}. Square roots of negative numbers can be discussed within the framework of complex numbers. Square roots of objects other than numbers can also be defined.

Square roots of integers that are not perfect squares are always irrational numbers: numbers not expressible as a ratio of two integers. For example, sqrt 2 cannot be written exactly as m/n, where n and m are integers. Nonetheless, it is exactly the length of the diagonal of a square with side length 1. This has been known since ancient times, with the discovery that sqrt 2 is irrational attributed to Hipparchus, a disciple of Pythagoras. (See square root of 2 for proofs of the irrationality of this number.)

Properties

The principal square root function f(x) = sqrt{x} (usually just referred to as the "square root function") is a function which maps the set of non-negative real numbers mathbb{R}^+ cup {0} onto itself, and, like all functions, always returns a unique value. The square root function also maps rational numbers into algebraic numbers (a superset of the rational numbers); sqrt x is rational if and only if x is a rational number which can be represented as a ratio of two perfect squares. In geometrical terms, the square root function maps the area of a square to its side length.

For all positive real numbers x and y, sqrt{xy} = sqrt x sqrt y and sqrt x = x^{1/2}.

sqrt{x^2} = x only when x ge 0; in general, sqrt{x^2} = left|xright| (see absolute value).

The square root function is continuous for all non-negative x, and differentiable for all positive x. Its derivative is given by f'(x) = tfrac{1}{2sqrt x}.

The Taylor series of sqrt{x+1} about x=0! is 1 + frac{1}{2}x - frac{1}{8}x^2 + frac{1}{16} x^3 - frac{5}{128} x^4 + dots! and converges for left| x right| < 1.

Computation

Many methods of calculating square roots exist today, some meant to be done by hand and some meant to be done by machine.

Many, but not all pocket calculators have a square root key. Computer spreadsheets and other software are also frequently used to calculate square roots. Computer software programs typically implement good routines to compute the exponential function and the natural logarithm or logarithm, and then compute the square root of x using the identity

sqrt{x} = e^{frac{1}{2}ln x} or sqrt{x} = 10^{frac{1}{2}log x}

The same identity is exploited when computing square roots with logarithm tables or slide rules.

The most common method of square root calculation by hand is known as the "Babylonian method". It involves a simple algorithm, which results in a number closer to the actual square root each time it is repeated. To find r, the square root of a real number x:

Start with an arbitrary positive start value r (the closer to the square root of x, the better).

Replace r by the average between r and x / r. (It is sufficient to take an approximate value of the average, not too close to the previous value of r and x / r in order to ensure convergence.)

Repeat step 2 until r and x / r are as close as desired.

The best known time complexity for computing a square root with n digits of precision is the same as that for multiplying two n-digit numbers.

2 times 12 equals 24. The square root of 24 is 4.9

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RE:

what is the square root of 2 times 12?

What is the square root of 2 times 12? I need help because i cant figure it out. please show the work

12 times the square root of 2 IS 12 times the square root of 2.

12sqrt(2) is the answer. It is an irrational number, therefore decimal representations are approximations.

2 X 12=24

square root the 24 by using a calculator or a scientific calculator

then, u will get 4.9

Do you need it in an exact answer, or a decimal? If a decimal, see some of the other answers. But if you need it in an exact answer, I'll try to show you how (though it's a bit difficult being unable to type a radical sign. Instead, I'll use 24^1/2, because anything to the 1/2 power is taking the square root...just try it in your calculator if you don't understand me, confusing as I am.)

(2 * 12) ^ 1/2 = 24 ^ 1/2 [Multiply everything under the radical]

24^1/2 = (4)^1/2 * (6)^1/2 [Factor out a perfect square]

2 * (6)^1/2 [Because you can pull out factors to make perfect squares, 4^1/2 becomes 2, leaving the square root of six with it. Thus, 2 times the square root of six becomes your final, exact answer.]

Interesting question. The answers up there are unbelievabe. They actually thought you meant sqrt (24). You should've used parentheses to make it clear you meant sqrt(2) X 12.

Let's see what can be done with it.

sqrt(2) X 12 =

sqrt(2) X 2 X 2 X 3

2 is actually sqrt()2)*sqrt(2), so we have five sqrt(2)'s in all, times 3.

So sqrt(2) X 12 is also 2^(5/2) X 3. This is one of the ways you could restate sqrt(2)*12... there are more... you get the idea...

your question can be interpreted two ways mathematically:

sqrt (2) x 12 = 1.41 x 12 = 16.97 or

sqrt (2 x 12) = sqrt (24) = 4.9

you have not given enough information.

use a calculator

I would use a calculator for this

just grab a calculator......