Which option is both real and irrational?
Answer and explanation
Correct answer: √18
A real number is any number that can be located on the real number line, while an irrational number cannot be written as p/q, where p and q are integers and q is non-zero. Since 18 = 9 × 2, √18 = 3√2. The number √2 is irrational, and multiplying it by the non-zero rational number 3 keeps it irrational; therefore √18 is real and irrational. Option B equals 1, option C also equals 1, and option D equals √100 ÷ √100 = 10 ÷ 10 = 1. These three values are rational, so option A is the only correct choice.
Frequently asked questions
What is the correct answer to this question?
√18
Why is this the correct answer?
A real number is any number that can be located on the real number line, while an irrational number cannot be written as p/q, where p and q are integers and q is non-zero. Since 18 = 9 × 2, √18 = 3√2. The number √2 is irrational, and multiplying it by the non-zero rational number 3 keeps it irrational; therefore √18 is real and irrational. Option B equals 1, option C also equals 1, and option D equals √100 ÷ √100 = 10 ÷ 10 = 1. These three values are rational, so option A is the only correct choice.
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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