Solve sqrt{3r}=sqrt{4r-1}

$$\sqrt { 3 r } = \sqrt { 4 r - 1 }$$

Solve for r

$$r=1$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3r}\right)^{2}=\left(\sqrt{4r-1}\right)^{2}$$

Calculate \sqrt{3r} to the power of 2 and get 3r.

$$3r=\left(\sqrt{4r-1}\right)^{2}$$

Calculate \sqrt{4r-1} to the power of 2 and get 4r-1.

$$3r=4r-1$$

Subtract 4r from both sides.

$$3r-4r=-1$$

Combine 3r and -4r to get -r.

$$-r=-1$$

Multiply both sides by -1.

$$r=1$$

Substitute 1 for r in the equation \sqrt{3r}=\sqrt{4r-1}.

$$\sqrt{3\times 1}=\sqrt{4\times 1-1}$$

Simplify. The value r=1 satisfies the equation.

$$3^{\frac{1}{2}}=3^{\frac{1}{2}}$$

Equation \sqrt{3r}=\sqrt{4r-1} has a unique solution.

$$r=1$$