The problem asks us to evaluate the expression $\sqrt{8.357} \times 0.895^2$.

ArithmeticSquare RootExponentsNumerical CalculationApproximation
2025/4/28

1. Problem Description

The problem asks us to evaluate the expression 8.357×0.8952\sqrt{8.357} \times 0.895^2.

2. Solution Steps

Let x=8.357×0.8952x = \sqrt{8.357} \times 0.895^2. We want to calculate the value of xx.
First, we calculate the square root of 8.3578.357:
8.3572.89084766\sqrt{8.357} \approx 2.89084766
Next, we calculate 0.89520.895^2:
0.8952=0.895×0.895=0.8010250.895^2 = 0.895 \times 0.895 = 0.801025
Finally, we multiply these two results:
x=2.89084766×0.8010252.31562022x = 2.89084766 \times 0.801025 \approx 2.31562022

3. Final Answer

x2.31562022x \approx 2.31562022
Rounding to four decimal places gives 2.31562.3156.
Therefore, 8.357×0.89522.3156\sqrt{8.357} \times 0.895^2 \approx 2.3156

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