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If (\sqrt{n}) lies between (10) and (11), which value of (n) can be correct and makes (\sqrt{n}) irrational?
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Answer and explanation
Correct answer: (105)
Step 1: (10<\sqrt{n}<11) means (100<n<121). Step 2: (105) lies in this interval and is not a perfect square, so (\sqrt{105}) is irrational. Step 3: Square both bounds to handle square-root ranges.
Frequently asked questions
What is the correct answer to this question?
(105)
Why is this the correct answer?
Step 1: (10<\sqrt{n}<11) means (100<n<121). Step 2: (105) lies in this interval and is not a perfect square, so (\sqrt{105}) is irrational. Step 3: Square both bounds to handle square-root ranges.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
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