Question
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
A. square root of 36
B. square root of 74
C. 3 square root 64
D. 2 square root 3
Answers
GPT-4o mini
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
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