Which option is the value of √24 × √6?
Answer and explanation
Correct answer: 12
Use the square-root product rule for non-negative numbers: √a × √b = √(ab). Thus √24 × √6 = √(24 × 6) = √144 = 12. A second check is possible by writing √24 = 2√6; then (2√6)(√6) = 2 × 6 = 12. Option B equals 6√24 and is not the value of the full product; it would be much larger. Option C incorrectly combines the radicands as 24 + 6 or otherwise fails to apply the multiplication rule. Option D also leaves an unnecessary radical factor and does not equal 12. Therefore the exact simplified value is the rational integer 12, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Use the square-root product rule for non-negative numbers: √a × √b = √(ab). Thus √24 × √6 = √(24 × 6) = √144 = 12. A second check is possible by writing √24 = 2√6; then (2√6)(√6) = 2 × 6 = 12. Option B equals 6√24 and is not the value of the full product; it would be much larger. Option C incorrectly combines the radicands as 24 + 6 or otherwise fails to apply the multiplication rule. Option D also leaves an unnecessary radical factor and does not equal 12. Therefore the exact simplified value is the rational integer 12, so option A is correct.
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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