So Radicals and Quadratic Functions Solve for \( v \), where \( v \) is a real number. \[ 8-\sqrt{v}=\sqrt{v-32} \] If there is more that one solution with two radicals that simplifies to sqrt( x\( )=\mathrm{a} \) If there is no solution, click on "No solution".

To solve the equation \( 8 - \sqrt{v} = \sqrt{v - 32} \), we can start by isolating one of the radicals on one side. 1. Rearranging gives us \( \sqrt{v - 32} = 8 - \sqrt{v} \). 2. Squaring both sides results in \( v - 32 = (8 - \sqrt{v})^2 \). 3. Expanding the right side: \( v - 32 = 64 - 16\sqrt{v} + v \). 4. This simplifies to \( -32 = 64 - 16\sqrt{v} \), leading to \( 16\sqrt{v} = 96 \). 5. Dividing both sides by 16 yields \( \sqrt{v} = 6 \). 6. Squaring both sides gives \( v = 36 \). We need to check if this value satisfies the original equation: - Substituting \( v = 36 \): \( 8 - \sqrt{36} = 8 - 6 = 2 \). - And \( \sqrt{36 - 32} = \sqrt{4} = 2 \). Both sides equal 2, so \( v = 36 \) is a valid solution. There’s only one solution here.