Math  /  Numbers & Operations

QuestionApproximate each number using a calculator. 525^{\sqrt{2}} 5211.0905^{\sqrt{2}} \approx 11.090 (Round to three decimal places.)

Studdy Solution

STEP 1

1. The problem requires us to approximate the value of 525^{\sqrt{2}} using a calculator.
2. The answer should be rounded to three decimal places.

STEP 2

1. Compute the square root of 2.
2. Raise 5 to the power of the computed square root of 2.
3. Round the result to three decimal places.

STEP 3

Compute the square root of 2 using a calculator.
21.414 \sqrt{2} \approx 1.414

STEP 4

Use a calculator to raise 5 to the power of the computed square root of 2.
5251.41411.090 5^{\sqrt{2}} \approx 5^{1.414} \approx 11.090

STEP 5

Round the result to three decimal places.
The approximate value of 525^{\sqrt{2}} is 11.090 \boxed{11.090} .

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