Question

Solve for y.

36y2 − 81 = 0

Write your answers as integers or as proper or improper fractions in simplest form.

y =
or y =

Answer 1

To solve the equation \( 36y^2 - 81 = 0 \), we can start by isolating the term with \( y \).

1. Add 81 to both sides:
\[
36y^2 = 81
\]

2. Divide both sides by 36 to solve for \( y^2 \):
\[
y^2 = \frac{81}{36}
\]

3. Simplify \( \frac{81}{36} \):
\[
y^2 = \frac{81 \div 9}{36 \div 9} = \frac{9}{4}
\]

4. Now take the square root of both sides. Remember to include both the positive and negative roots:
\[
y = \pm \sqrt{\frac{9}{4}} = \pm \frac{\sqrt{9}}{\sqrt{4}} = \pm \frac{3}{2}
\]

So the solutions for \( y \) are:
\[
y = \frac{3}{2} \quad \text{or} \quad y = -\frac{3}{2}
\]

Finally, the answers are:
\[
y = \frac{3}{2} \quad \text{or} \quad y = -\frac{3}{2}
\]