Determine whether each expression is rational or irrational.

A. square root of 36

B. square root of 74

C. 3 square root 64

D. 2 square root 3

1 answer

To determine whether each expression is rational or irrational, we need to analyze each one:

A. Square root of 36:
\(\sqrt{36} = 6\), which is a whole number. Therefore, it is a rational number.

B. Square root of 74:
\(\sqrt{74}\) is not a perfect square, and its decimal expansion is non-repeating and non-terminating. Therefore, it is an irrational number.

C. 3 square root of 64:
This can be expressed as \(3 \times \sqrt{64} = 3 \times 8 = 24\). Since 24 is a whole number, it is a rational number.

D. 2 square root of 3:
This can be expressed as \(2 \times \sqrt{3}\). Since \(\sqrt{3}\) is known to be an irrational number, multiplying it by 2 (a rational number) still results in an irrational number. Therefore, \(2\sqrt{3}\) is irrational.

In summary: A. Rational
B. Irrational
C. Rational
D. Irrational