Pi is about 3.14159265. You can round that to as many or as few significant digits are are appropriate for a particular application.
The square root of 2 and the value of pi are two examples of irrational numbers which can't be expressed as fractions
[pi^(1/3)]^2 * pi = pi^(2/3) * pi = pi^(5/3) The answer is the cubic root of pi to the fifth power.
(pi + pi + pi) = 3 pi = roughly 9.4248 (rounded) Well, if you use the common shortened version of pi which is 3.14 and add that 3 times, you get 9.42.
(cos(pi x) + sin(pi y) )^8 = 44 differentiate both sides with respect to x 8 ( cos(pi x) + sin (pi y ) )^7 d/dx ( cos(pi x) + sin (pi y) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (-sin (pi x) pi + cos (pi y) pi dy/dx ) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (pi cos(pi y) dy/dx - pi sin (pi x) ) = 0 cos(pi y) dy/dx - pi sin(pi x) = 0 cos(pi y) dy/dx = sin(pi x) dy/dx = sin (pi x) / cos(pi y)
Einstein may have used pi (Ï€)in his equations but he had no involvement in the creation or application of pi.
Perhaps the best know application is the use of Pi in relation to circles and spheres
Pi is about 3.14159265. You can round that to as many or as few significant digits are are appropriate for a particular application.
Pi, being irrational, has an endless number of digits to the right of the decimal, as you know. But for almost any application, even basic engineering, a value of 3.1417 is highly accurate.
Pi-R-Squared. pi*R^2 That's the formula for area of a circle, where R=radius. For R=7 the formula gives 49pi. Some calculators have pi buttons, but estimating pi=3.14 is often close enough for real-world application. 49*3.14 = almost 154 square feet.
The square root of 2 and the value of pi are two examples of irrational numbers which can't be expressed as fractions
(pi)(1/pi)=1.4396 ...
This is an opinion. While it is more of a mathematical 'trivial pursuit' now. I don't know of any application that could possibly need the value of pi to 1000 or 1 million or more digits. However, computing pi decimal value has been used to test speed and accuracy of new computer processors and algorithms.
the same as pi squared, which is 9.86960440109
Some details you may want to know: pi indicates the ratio of the circumference to the diameter in a circle; pi is irrational (you can't express it as the ratio of two integers) and trascendental (nor as the solution of a polynomial equation). Irrational also means that the digits won't repeat indefinitely. With trigonometric formulae and powerful computers, pi has already been calculated to over a billion digits. Knowing these digits, by itself, has no practical application.
The square root of pi times pi is simply pi. Because pi*pi=pi squared, the squared and the square root will cancel each other, leaving just pi.
Pi to the 5th power is approximately 306.019684785