Round a Root after Locating It

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: Approximate √6 to the nearest tenth; a calculator may be used. Candidate answers: (A) 2 (B) 2.4 (C) 3 (D) 4.4.
• Independent check inputs: Approximate √11 to the nearest tenth; a calculator may be used. Candidate answers: (A) 3 (B) 3.3 (C) 4 (D) 5.5.

Learn the idea

Roots reverse powers, but their exact values and decimal approximations must be distinguished. Integer squares provide reliable bounds, and odd roots retain negative signs while principal square roots are nonnegative. A decimal root approximation can be checked against whole-number bounds before rounding. The requested precision describes the reported approximation, not a change in the exact mathematical value.

Here is the method on the supplied teaching case. The exact root lies between 2 and 3. Its decimal value is approximately 2.449490; rounding the hundredths place gives 2.4.

Round only after calculating enough digits, and retain a calculator value through intermediate work when needed. State that the rounded value is approximate rather than writing it as an exact radical equality.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: Approximate √83 to the nearest tenth; a calculator may be used. Candidate answers: (A) 10 (B) 41.5 (C) 9 (D) 9.1. Show the mathematical reason, not only the selected answer. Expected result: 9.1. The exact root lies between 9 and 10. Its decimal value is approximately 9.110434; rounding the hundredths place gives 9.1.

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