Question

Which expressions simplify to a rational answer?

Select each correct answer.



3‾√·2‾√

11‾‾‾√·5‾√

52·‾‾√2‾√

9‾√·16‾‾‾√

Answer 1

sqrt(3) * sqrt(2) = sqrt(6) is irrational
sqrt(11) * sqrt(5) = sqrt(55) is irrational
5sqrt(2) * sqrt(2) = 5sqrt(4) = 5 * 2 = 10 is rational
sqrt(144) = 12 is rational

Answer 2

Answer: Expression  $\sqrt{9}.\sqrt{16}$  will be the correct answer.

Explanation:

Since, we know that a rational Number is a number which can be expressed in the form p/q where q≠0 .

here the option √3×√2=√6 is not a rational number.(because, $=\sqrt{m} \times \sqrt{n}= \sqrt{m\times n}$)

√11×√5=√55 is not a rational number.

√52×√2=√104 is not a rational number.

√9×√16=√144=12 is a rational number. ( because every integer must be a rational number).

So, 4th option will be correct .