Question

find the error kendra states that \\(\sqrt{3} > 2\\) because 3 is greater than 2. choose the response that explains kendra’s mistake and corrects it.\
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\\(\bigcirc\\) a) kendra did not estimate the square root of 3. since \\(\sqrt{3}\\) is 9 and 9 is greater than 2, \\(\sqrt{3} > 2\\).\
\\(\bigcirc\\) b) kendra did not estimate the square root of 3. since \\(\sqrt{3}\\) is approximately 1.73 and 1.73 is less than 2, \\(\sqrt{3} < 2\\)\
\\(\bigcirc\\) c) kendra did not estimate the square root of 3. since \\(\sqrt{3}\\) is approximately 2.73 and 2.73 is greater than 2, \\(\sqrt{3} > 2\\).\
\\(\bigcirc\\) d) kendra did not estimate the square root of 2 or 3. since \\(\sqrt{2}\\) is approximately 1.41 and \\(\sqrt{3}\\) is approximately 1.73 and 1.73 is greater than 1.41, \\(\sqrt{3} > 2\\)

Explanation:

To determine the mistake, we analyze the square root of 3. The square root of a number \( n \) (where \( n \) is not a perfect square) needs to be estimated. We know that \( \sqrt{1} = 1 \), \( \sqrt{4}=2 \), and since \( 1 < 3 < 4 \), \( \sqrt{1}<\sqrt{3}<\sqrt{4} \), so \( 1 < \sqrt{3}< 2 \). The approximate value of \( \sqrt{3} \) is 1.73, which is less than 2.

• Option A is wrong because \( (\sqrt{3})^2 = 3 \), not \( \sqrt{3}=9 \).
• Option C is wrong because \( \sqrt{3}\approx1.73 \), not 2.73.
• Option D is irrelevant as we are comparing \( \sqrt{3} \) with 2, not with \( \sqrt{2} \).

So the correct option is B.

Answer:

B) Kendra did not estimate the square root of 3. Since \( \sqrt{3} \) is approximately 1.73 and 1.73 is less than 2, \( \sqrt{3}<2 \)