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 that needs to be approximated: \(3^{\sqrt{5}}\).
2. Calculate \(\sqrt{5}\) using a calculator to find the square root of 5.
3. Raise 3 to the power of the result from the previous step. This means you will calculate \(3^{\text{(result from step 2)}}\).
4. Use a calculator to perform the exponentiation and obtain a decimal approximation.
5. Round the result from the previous step to three decimal places.

Key Concepts

Exponents and Roots

Exponents represent repeated multiplication of a number, while roots indicate the inverse operation. In the expression 3^√5, the base is 3, and the exponent is the square root of 5. Understanding how to manipulate exponents and roots is crucial for evaluating expressions involving them.

Calculator Functions

Using a calculator effectively requires familiarity with its functions, especially for operations involving exponents and roots. Most scientific calculators have specific buttons for exponentiation and square roots, which allow for accurate computation of expressions like 3^√5. Knowing how to input these operations is essential for obtaining the correct result.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of precision, in this case, to three decimal places. This involves looking at the digit in the fourth decimal place to determine whether to round up or down. Mastery of rounding is important for presenting numerical results clearly and accurately, especially in mathematical contexts.