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Approximate each number using a calculator. Round your answer to three decimal places. $$3^{\sqrt{5}}$$

Short Answer

Expert verified
So, the approximation for \(3^{\sqrt{5}}\) rounded to three decimal places is 12.916.

Step by step solution

01

Evaluate Square Root

Use the calculator to find the square root of 5. This gives a value approximately equal to 2.236.
02

Exponentiation

Next, calculate \(3^{2.236}\). The calculator gives a result of approximately 12.915.
03

Rounding

Finally, round the final result to three decimal places. The '5' in the fourth decimal place means the preceding number, which is '1', is increased by 1, giving the final rounded answer of 12.916.

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