Evaluate the square root of 0.4 correct up to two decimal places.
The correct answer and explanation is:
To find the square root of 0.4, you can use a calculator or apply the long division method for square roots. The square root of 0.4, rounded to two decimal places, is approximately 0.63.
Explanation:
The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, you are looking for a number that, when squared, equals 0.4. Mathematically, you are solving the equation: Let x=0.4 ⟹ x2=0.4\text{Let} \, x = \sqrt{0.4} \implies x^2 = 0.4
To approximate this value, you can use a calculator or numerical methods like the Newton-Raphson method. For simplicity, let’s use the calculator result for this example, which gives 0.6324555320. Rounding this to two decimal places, we get 0.63.
To verify the result, square 0.63: 0.632=0.3969≈0.40.63^2 = 0.3969 \approx 0.4
Thus, 0.63 is a reasonable approximation of the square root of 0.4, accurate to two decimal places.
Square roots are essential in various fields such as physics, engineering, and finance. In practice, square roots are used to calculate things like areas, distances, and solutions to certain equations. In this example, understanding how to find the square root of a non-perfect square (like 0.4) is important because it demonstrates how to handle irrational numbers, which cannot be expressed exactly as fractions or decimals. Therefore, rounding to the desired number of decimal places is a useful and common approach.