Question

Solve the equation by finding square roots.one fiftht Superscript 2minus4equals0Question content area bottomPart 1Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.A.tequalsenter your response here​(Type an integer or decimal rounded to the nearest tenth as needed. Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \( \frac{1}{5} t^2 - 4 = 0 \), follow these steps:

1. **Isolate the term with \( t^2 \)**:
\[
\frac{1}{5} t^2 = 4
\]

2. **Multiply both sides by 5 to eliminate the fraction**:
\[
t^2 = 20
\]

3. **Take the square root of both sides**:
\[
t = \pm \sqrt{20}
\]

4. **Simplify \( \sqrt{20} \)**:
\[
\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}
\]

5. **So the solutions are**:
\[
t = 2\sqrt{5} \quad \text{and} \quad t = -2\sqrt{5}
\]

Now, we can approximate \( 2\sqrt{5} \) using a calculator. Knowing that \( \sqrt{5} \approx 2.236 \):
\[
2\sqrt{5} \approx 2 \times 2.236 = 4.472
\]

Thus, rounding to the nearest tenth gives:
\[
t \approx 4.5 \quad \text{and} \quad t \approx -4.5
\]

**Final Answer**:
The complete solution is:
\[
t \approx 4.5, -4.5
\]
You can input this as:
\( t = 4.5, -4.5 \)