Select the correct answer. Estimate the value of [tex]$\frac{\sqrt{2} \pi}{\sqrt{5}}$[/tex]
A. 0.33
B. 0.50
C. 0.67
D. 2.0
Answer (2)
Approximate 2 as 1.414, π as 3.142, and 5 as 2.236.
Substitute these approximations into the expression: 2.236 1.414 × 3.142 .
Calculate the result: 2.236 1.414 × 3.142 ≈ 1.99 .
Choose the option closest to the calculated value: 2.0 .
Explanation
Understanding the Problem We are asked to estimate the value of the expression 5 2 π and choose the closest option from the given choices.
Approximating Values We can approximate the values of 2 , π , and 5 to simplify the calculation. From the tool, we have 2 ≈ 1.414 , π ≈ 3.142 , and 5 ≈ 2.236 .
Substituting Approximations Substitute these approximations into the expression: 5 2 π ≈ 2.236 1.414 × 3.142
Calculating the Numerator Calculate the numerator: 1.414 × 3.142 ≈ 4.449
Dividing Numerator by Denominator Divide the numerator by the denominator: 2.236 4.449 ≈ 1.99 From the tool, we have 2.23606797749979 1.4142135623730951 ∗ 3.141592653589793 ≈ 1.987
Choosing the Closest Option The closest option to the calculated value of approximately 1.99 is 2.0.
Examples
Estimating values like this is useful in everyday situations, such as when you're cooking and need to quickly adjust a recipe, or when you're shopping and want to compare prices. For example, if you know the price of an item in one currency and want to estimate its price in another currency, you can use approximations to quickly get a sense of the cost.
To estimate 5 2 π , we approximate the values giving approximately 1.99. The closest multiple-choice option is 2.0, so that is the correct answer.
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