Solve each equation for the specified variable. (Assume all denominators are nonzero.) d=k√h, for h

Verified step by step guidance

1. Start with the given equation: \(d = k \sqrt{h}\).
2. Isolate the square root term by dividing both sides of the equation by \(k\): \(\frac{d}{k} = \sqrt{h}\).
3. To eliminate the square root, square both sides of the equation: \(\left( \frac{d}{k} \right)^2 = h\).
4. Simplify the right side to express \(h\) explicitly: \(h = \left( \frac{d}{k} \right)^2\).
5. State the final expression for \(h\) in terms of \(d\) and \(k\): \(h = \frac{d^2}{k^2}\).

Key Concepts

Isolating the Variable

Isolating the variable means rearranging the equation to express the specified variable alone on one side. This involves using inverse operations such as division, multiplication, or taking roots to undo operations applied to the variable.

Square Root and Squaring

The square root function, denoted by √, is the inverse of squaring a number. To solve for a variable inside a square root, you often square both sides of the equation to eliminate the root, remembering to consider domain restrictions.

Properties of Equality

Properties of equality allow you to perform the same operation on both sides of an equation without changing its solution. This principle is essential for manipulating equations correctly when isolating variables.