Which option gives the product of √3 and √27?
Answer and explanation
Correct answer: 9
For non-negative radicands, the product rule √a × √b = √(ab) applies. Therefore √3 × √27 = √(3 × 27) = √81 = 9. The same result can be seen by simplifying √27 = 3√3, giving √3 × 3√3 = 3 × 3 = 9. Option B, 3√3, is only the simplified form of √27 by itself and does not include the remaining multiplication by √3. Option C incorrectly multiplies the radicands as 3 × 27 = 30, while option D introduces an unnecessary factor. Since 9 is rational and an integer, option A is the correct product.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
For non-negative radicands, the product rule √a × √b = √(ab) applies. Therefore √3 × √27 = √(3 × 27) = √81 = 9. The same result can be seen by simplifying √27 = 3√3, giving √3 × 3√3 = 3 × 3 = 9. Option B, 3√3, is only the simplified form of √27 by itself and does not include the remaining multiplication by √3. Option C incorrectly multiplies the radicands as 3 × 27 = 30, while option D introduces an unnecessary factor. Since 9 is rational and an integer, option A is the correct product.
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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