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.)

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.)

GPT-4o mini · Answer

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 $