Which of the following is an irrational number between 6 and 7?
Answer and explanation
Correct answer: \(\sqrt{43}\)
\(\sqrt{43}\) is between 6 and 7 because 36 < 43 < 49 implies \(\sqrt{36}=6 < \sqrt{43} < \sqrt{49}=7\). Since 43 is not a perfect square, \(\sqrt{43}\) is irrational. Checking other options: \(\sqrt{36}=6\) equals the lower endpoint, \(\sqrt{50}\approx7.07\) is greater than 7, and \(13/2=6.5\) is rational even though it lies between 6 and 7. Exam tip: compare under-the-root numbers with nearest perfect squares to locate square roots and test for irrationality by checking for perfect squares.
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{43}\)
Why is this the correct answer?
\(\sqrt{43}\) is between 6 and 7 because 36 < 43 < 49 implies \(\sqrt{36}=6 < \sqrt{43} < \sqrt{49}=7\). Since 43 is not a perfect square, \(\sqrt{43}\) is irrational. Checking other options: \(\sqrt{36}=6\) equals the lower endpoint, \(\sqrt{50}\approx7.07\) is greater than 7, and \(13/2=6.5\) is rational even though it lies between 6 and 7. Exam tip: compare under-the-root numbers with nearest perfect squares to locate square roots and test for irrationality by checking for perfect squares.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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