What is the value of √2 × √50?
Answer and explanation
Correct answer: 10
The governing concept is the product rule for square roots: for non-negative numbers, √a × √b = √(ab). Applying it gives √2 × √50 = √(2 × 50) = √100 = 10, because the principal square root of 100 is 10. Therefore option D is correct. The result can also be checked by simplifying √50 first: √50 = √(25 × 2) = 5√2. Hence √2 × √50 = √2 × 5√2 = 5(√2)² = 5 × 2 = 10. Option A incorrectly treats the factors as if their square roots produced 25. Option B is only an intermediate expression before multiplying the remaining surds, so it is not the final value. Option C incorrectly adds the radicands instead of multiplying them.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The governing concept is the product rule for square roots: for non-negative numbers, √a × √b = √(ab). Applying it gives √2 × √50 = √(2 × 50) = √100 = 10, because the principal square root of 100 is 10. Therefore option D is correct. The result can also be checked by simplifying √50 first: √50 = √(25 × 2) = 5√2. Hence √2 × √50 = √2 × 5√2 = 5(√2)² = 5 × 2 = 10. Option A incorrectly treats the factors as if their square roots produced 25. Option B is only an intermediate expression before multiplying the remaining surds, so it is not the final value. Option C incorrectly adds the radicands instead of multiplying them.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Real Numbers.
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