What type of number is the product of \(\sqrt{2}\) and \(\sqrt{8}\)?
Answer and explanation
Correct answer: Rational number
\(\sqrt{2}\times\sqrt{8}=\sqrt{2\times8}=\sqrt{16}=4\). Since \(4=\frac{4}{1}\), it is a rational number. Although \(\sqrt{2}\) and \(\sqrt{8}\) are individually irrational, the product of two irrational numbers is not always irrational. Also, \(4\) is neither negative nor non-real. Exam tip: When multiplying square roots, multiply the radicands first and look for a perfect square.
Frequently asked questions
What is the correct answer to this question?
Rational number
Why is this the correct answer?
\(\sqrt{2}\times\sqrt{8}=\sqrt{2\times8}=\sqrt{16}=4\). Since \(4=\frac{4}{1}\), it is a rational number. Although \(\sqrt{2}\) and \(\sqrt{8}\) are individually irrational, the product of two irrational numbers is not always irrational. Also, \(4\) is neither negative nor non-real. Exam tip: When multiplying square roots, multiply the radicands first and look for a perfect square.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Rational numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
