If you have a non-scientific calculator you can use the Newton-Raphson method.
Let f(x) = x2 - 800, and f'(x) = 2x
[f'(x) is the derivative of f(x) but you do not need to know that to use the N-R method.]
Make a guess at the square root of 800, and call is x0.
Then calculate
xn+1 = xn - f(xn)/f'(xn) for n = 1, 2, 3, ...
Provided you made a reasonable choice for the starting point, the iteration will very quickly converge to the true answer. Even if it is not so good:
Suppose you start with x0 = 20 (a pretty poor choice since 202 is 400, which is nowhere near 800).
Even so, x3 = 2.843 is less than 1 in 24 thousand from the true value and x4 has an error of less than 1 in 30 billion.
sqrt(800) + sqrt(50) - sqrt(18) = 31.113 approximately.
Press the square root button on your calculator.
The square root of 289 is ± 17.
The square root of 1225 is 35.
The square root of 8649 is 93.
The square root of 800: ± 28.284271
sqrt(800) + sqrt(50) - sqrt(18) = 31.113 approximately.
The square root of 1800 is 90
800
20 times the square root of 2
Take the square root of 800, and the square root of 900. Look for an integer between the two.
There is two ways to interpret "5 radical sign'. It can either mean: five times the square root of 800 leading to: √(5 × √800) ≈ 11.8921 or, if the five is small and raised slightly it is the fifth root of 800 and it leads to: √(fifth_root(800)) = (800^(1/5))^(1/2) = 800^(1/10) ≈ 1.9512
find the square root of the numerator and the square root of the denominator
Press the square root button on your calculator.
Find the square root of each of its components, and muliply them together. For example, 36x8 the square root of 36 is 6 the square root of x8 is x4 so the square root of 36x8 is 6x4
Do the addition, get the answer and then find its square root!
The square root of 289 is ± 17.