Solve sqrt(1/2*(1-1/k))

Evaluate

\frac{1}{2} (1 - \frac{1}{k})

To find the roots of the expression,set the expression equal to 0

\frac{1}{2} (1 - \frac{1}{k}) = 0

Find the domain

More Steps

\frac{1}{2} (1 - \frac{1}{k}) = 0, k \in (- \infty, 0) \cup [1, + \infty)

Calculate

\frac{1}{2} (1 - \frac{1}{k}) = 0

Subtract the terms

More Steps

\frac{1}{2} \times \frac{k - 1}{k} = 0

Multiply the terms

\frac{k - 1}{2 k} = 0

The only way a root could be 0 is when the radicand equals 0

\frac{k - 1}{2 k} = 0

Cross multiply

k - 1 = 2 k \times 0

Simplify the equation

k - 1 = 0

Move the constant to the right side

k = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

k = 1

Check if the solution is in the defined range

k = 1, k \in (- \infty, 0) \cup [1, + \infty)

Solution

k = 1

Sqrt(1/2*(1 1/k))