Which option correctly describes the nature of (\frac{\sqrt{18}}{\sqrt{5}})?
Answer and explanation
Correct answer: Irrational because (\frac{18}{5}) is not a perfect square
Step 1: (\frac{\sqrt{18}}{\sqrt{5}}=\sqrt{\frac{18}{5}}). Step 2: (\frac{18}{5}) is not a perfect square of a rational number, so the result is irrational. Step 3: In quotients of radicals, check whether the fraction inside is a perfect square.
Frequently asked questions
What is the correct answer to this question?
Irrational because (\frac{18}{5}) is not a perfect square
Why is this the correct answer?
Step 1: (\frac{\sqrt{18}}{\sqrt{5}}=\sqrt{\frac{18}{5}}). Step 2: (\frac{18}{5}) is not a perfect square of a rational number, so the result is irrational. Step 3: In quotients of radicals, check whether the fraction inside is a perfect square.
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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