4.486
The 8th root
The principal square root is the non-negative square root.
To simplify the square root of 5 times the square root of 6, you can multiply the two square roots together. This gives you the square root of (5*6), which simplifies to the square root of 30. Therefore, the simplified answer is the square root of 30.
No. The Square root of x is not the value of x. So it can not be simplified beyond: Root X + root 3x Yes. The square root of 3x equals the square root of 3 times the square root of x, so when you add another square root of x, you can factor out the square root of x, thereby simplifying the expression to the square root of x times the sum of one plus the square root of three.
81 is the square root of 405. (81 x 5 = 405.)
405 is exactly 9 times the square root of five . The square root of 5 is irrational and can only be approximated with decimals.
9 times the square root of 5
4.486
sin(405) = square root of 2 divided by 2 which is about 0.7071067812
5sqrt(405) = 5sqrt(815) = 5sqrt(81)sqrt(5) = 59sqrt(5) = 45sqrt(5)
GM of two numbers is the square root of their product, in this case sqrt 2025 ie 45.
The perimeter of a rectangle cannot be calculated by just knowing the area unless the rectangle is a square. In which case the perimeter will be 4 x square root of the area.
Best option is to use a calculator. Failing that, use the Newton-Raphson method which entails making a guess at the answer and then improving on it. Repeating the procedure should lead to a better estimate at each stage. To start with, if you want to find the square root of 405, define f(x) = x2 - 405. Then finding the square root of 405 is equivalent to solving f(x) = 0. Let f'(x) = 2x. This is the derivative of f(x) but you do not need to know that to use the N-R method. Start with x0 as the first guess. Then let xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, … After a few iterations, xn will be very close to the required square root. If you start with 20, whose square is 400, the second iteration gives a result that is accurate to 8 decimal places.
The square root of the square root of 2
The 8th root
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