Calculate the value of the expression $\sqrt{8.357 \times 0.895^2}$.

1. Problem Description

Calculate the value of the expression $\sqrt{8.357 \times 0.895^2}$.

2. Solution Steps

Let the expression be $x$.

$x = \sqrt{8.357 \times 0.895^2}$

$x = \sqrt{8.357} \times \sqrt{0.895^2}$

$x = \sqrt{8.357} \times 0.895$

To find the square root of $8.357$, we can approximate.

Since $2^2 = 4$ and $3^2 = 9$, $\sqrt{8.357}$ is between 2 and

3. Also, $2.8^2 = 7.84$ and $2.9^2 = 8.41$. Thus, $\sqrt{8.357}$ is close to 2.

9. Using a calculator, $\sqrt{8.357} \approx 2.890847638$.

$x \approx 2.890847638 \times 0.895$

$x \approx 2.586208635$

$x \approx 2.586$ (rounded to 3 decimal places).

Alternatively, we can approximate the square root of 8.357 as 2.

9. Then, $x \approx 2.9 \times 0.895 = 2.5955$.

Using a calculator, the original expression is $\sqrt{8.357 \times 0.895^2} = \sqrt{8.357 \times 0.801025} = \sqrt{6.694764425} \approx 2.587424305$

Rounding to 3 decimal places, the result is 2.

5

8

7.

3. Final Answer

2.587