Solve sqrt{29/4}=asqrt{b}

$$\sqrt { 29 / 4 } = a \sqrt { b }$$

Solve for a

$$a=\frac{\sqrt{\frac{29}{b}}}{2}$$

$$b>0$$

Steps for Solving Linear Equation

Rewrite the square root of the division \sqrt{\frac{29}{4}} as the division of square roots \frac{\sqrt{29}}{\sqrt{4}}.

$$\frac{\sqrt{29}}{\sqrt{4}}=a\sqrt{b}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{29}}{2}=a\sqrt{b}$$

Swap sides so that all variable terms are on the left hand side.

$$a\sqrt{b}=\frac{\sqrt{29}}{2}$$

Multiply both sides of the equation by 2.

$$2a\sqrt{b}=\sqrt{29}$$

The equation is in standard form.

$$2\sqrt{b}a=\sqrt{29}$$

Divide both sides by 2\sqrt{b}.

$$\frac{2\sqrt{b}a}{2\sqrt{b}}=\frac{\sqrt{29}}{2\sqrt{b}}$$

Dividing by 2\sqrt{b} undoes the multiplication by 2\sqrt{b}.

$$a=\frac{\sqrt{29}}{2\sqrt{b}}$$

Divide \sqrt{29} by 2\sqrt{b}.

$$a=\frac{29}{2\sqrt{29b}}$$

Solve for b

$$b=\frac{29}{4a^{2}}$$

$$a>0$$

Steps for Solving Radical Equations

Rewrite the square root of the division \sqrt{\frac{29}{4}} as the division of square roots \frac{\sqrt{29}}{\sqrt{4}}.

$$\frac{\sqrt{29}}{\sqrt{4}}=a\sqrt{b}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{29}}{2}=a\sqrt{b}$$

Swap sides so that all variable terms are on the left hand side.

$$a\sqrt{b}=\frac{\sqrt{29}}{2}$$

Multiply both sides of the equation by 2.

$$2a\sqrt{b}=\sqrt{29}$$

Divide both sides by 2a.

$$\frac{2a\sqrt{b}}{2a}=\frac{\sqrt{29}}{2a}$$

Dividing by 2a undoes the multiplication by 2a.

$$\sqrt{b}=\frac{\sqrt{29}}{2a}$$

Square both sides of the equation.

$$b=\frac{29}{4a^{2}}$$