What is (√27 ÷ 3) equal to?
Answer and explanation
Correct answer: √3
The governing concept is extraction of perfect-square factors from a radical, followed by ordinary division. Rewrite 27 as 9 × 3. Then √27 = √(9 × 3) = √9 × √3 = 3√3. Substituting this into the expression gives √27 ÷ 3 = (3√3) ÷ 3 = √3. Therefore option B is correct. Option A confuses the square root of 27 with a whole-number value, while option C is unrelated to the given division and is the square of 3. Option D is the reciprocal of √3, not √3 itself. Since 3 is not a perfect square, √3 cannot be simplified to an integer or terminating rational value and remains irrational in the final answer.
Frequently asked questions
What is the correct answer to this question?
√3
Why is this the correct answer?
The governing concept is extraction of perfect-square factors from a radical, followed by ordinary division. Rewrite 27 as 9 × 3. Then √27 = √(9 × 3) = √9 × √3 = 3√3. Substituting this into the expression gives √27 ÷ 3 = (3√3) ÷ 3 = √3. Therefore option B is correct. Option A confuses the square root of 27 with a whole-number value, while option C is unrelated to the given division and is the square of 3. Option D is the reciprocal of √3, not √3 itself. Since 3 is not a perfect square, √3 cannot be simplified to an integer or terminating rational value and remains irrational in the final answer.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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