Math  /  Algebra

QuestionSolve the following equation for uu. 8=auu=\begin{array}{l} 8=a \sqrt{u} \\ u=\square \end{array}

Studdy Solution

STEP 1

1. The equation 8=au 8 = a \sqrt{u} is a simple algebraic equation involving a square root.
2. We assume a0 a \neq 0 to avoid division by zero.

STEP 2

1. Isolate the square root term u\sqrt{u}.
2. Solve for u u .

STEP 3

First, isolate the square root term u\sqrt{u} by dividing both sides of the equation by a a :
8=au 8 = a \sqrt{u} 8a=u \frac{8}{a} = \sqrt{u}

STEP 4

To solve for u u , square both sides of the equation to eliminate the square root:
(8a)2=(u)2 \left(\frac{8}{a}\right)^2 = (\sqrt{u})^2 64a2=u \frac{64}{a^2} = u
The value of u u is:
u=64a2 u = \frac{64}{a^2}

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