Answer:
√5 is irrational
Step-by-step explanation:
A rational number is one that can be written exactly as an integer or ratio of integers. Written as a decimal number, it will have a finite number of digits, or a repeating decimal fraction.
<h3>Application</h3>
Usually, a number that can <em>only</em> be expressed <em>exactly</em> using a <em>symbol</em> will be irrational. For square roots, any root of an integer other than a perfect square will be irrational.
The integer 5 is not a perfect square. It is between the squares 2²=4 and 3²=9. The square root of 5 is irrational.
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<em>Additional comment</em>
A reduced fraction whose denominator has factors other than 2 or 5 will translate to a repeating decimal. The number of repeating digits may be as many as 1 less than the denominator. For example, 1/19 has an 18-digit repeating decimal equivalent.
452.16 = 3.1416 r^2
r^2 = 452.16 / 3.1416
r^2 = 143.93
r = 11.997
C = 2 (3.1416) (12) =75.38 m
