In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3^√5

Verified step by step guidance

1. Identify the expression to approximate: \(3^{\sqrt{5}}\) means 3 raised to the power of the square root of 5.
2. Calculate the square root of 5 using a calculator: find \(\sqrt{5}\).
3. Use the value of \(\sqrt{5}\) as the exponent and calculate \(3^{\text{(value of } \sqrt{5} \text{)}}\) using the calculator's exponentiation function.
4. Round the result to three decimal places as requested.
5. Write the final rounded value as the approximate answer.

Key Concepts

Exponents and Radicals

Exponents represent repeated multiplication, while radicals are the inverse operation, indicating roots. Understanding how to interpret expressions like 3 raised to the root of 5 is essential for evaluating such expressions accurately.

Using a Calculator for Approximation

Calculators can approximate values of expressions involving irrational numbers or roots. Knowing how to input roots and exponents correctly ensures accurate results, especially when exact values are not easily simplified.

Rounding to a Specified Decimal Place

Rounding involves adjusting a number to a certain number of decimal places for simplicity and clarity. Rounding to three decimal places means keeping three digits after the decimal point and adjusting the last digit based on the next digit's value.