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: \(\left( \frac{d}{k} \right)^2 = (\sqrt{h})^2\).
4. Simplify the right side since squaring the square root cancels out: \(\left( \frac{d}{k} \right)^2 = h\).
5. Rewrite the expression for \(h\) explicitly: \(h = \left( \frac{d}{k} \right)^2\).

Key Concepts

Isolating the Variable

Isolating the variable means rewriting the equation so that the variable of interest stands alone on one side. This often involves performing inverse operations such as division, multiplication, or taking roots to both sides to solve for the specified variable.

Square Root and Squaring

When a variable is under a square root, solving for it requires squaring both sides of the equation to eliminate the root. This step must be done carefully to maintain equality and consider the domain restrictions.

Domain Restrictions and Nonzero Denominators

Equations involving denominators or roots have domain restrictions to avoid division by zero or undefined expressions. It is important to assume denominators are nonzero and consider the domain of variables when solving.