Question

Determine whether each expression is rational or irrational.

A.√36_____________

B.√74_____________

C. 3^√64___________

D. ^3√3_____________

Answer 1

To determine whether each expression is rational or irrational, let's analyze them one by one.

A. \(\sqrt{36}\)

\(\sqrt{36} = 6\), which is a whole number. Whole numbers are rational numbers.

**Answer: Rational**

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B. \(\sqrt{74}\)

The number 74 is not a perfect square, so \(\sqrt{74}\) cannot be expressed as a fraction of two integers.

**Answer: Irrational**

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C. \(3^{\sqrt{64}}\)

First, evaluate \(\sqrt{64} = 8\). Thus, we have \(3^{\sqrt{64}} = 3^8\).

Since \(3^8 = 6561\), which is a whole number, it is also rational.

**Answer: Rational**

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D. \(\sqrt[3]{3}\)

The cube root of 3 is not a perfect cube, and it cannot be expressed as a fraction of two integers. Thus, \(\sqrt[3]{3}\) is an irrational number.

**Answer: Irrational**

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Summarizing:

A. Rational

B. Irrational

C. Rational

D. Irrational