Is

Question

\[\dfrac{36}{25}\cdot \sqrt{11}\] rational or irrational?
Choose 1 answer:
Choose 1 answer:
(Choice A) Rational
A
Rational
(Choice B) Irrational
B
Irrational
(Choice C) It can be either rational or irrational
C
It can be either rational or irrational

Answer 1

To determine whether the expression

\[ \dfrac{36}{25} \cdot \sqrt{11} \]

is rational or irrational, let's analyze each component of the expression:

1. Rational Number: The fraction \(\frac{36}{25}\) is a rational number because it is the quotient of two integers (36 and 25).

2. Irrational Number: The square root \(\sqrt{11}\) is an irrational number because 11 is not a perfect square.

Now, when we multiply a rational number by an irrational number, the result is always irrational. Therefore,

\[ \dfrac{36}{25} \cdot \sqrt{11} \]

must be irrational.

Thus, the correct choice is:

(Choice B) Irrational.