Irrational numbers are:
1-Not fractions
2-Non-terminating and non-repeating decimals
3-Radicals that do not simplify to whole numbers
4-All of the above.
http://www.mathsisfun.com/irrational-numbers.html
1 and 2
3 is false, since √2.25 = 1.5 is a radical that is not a whole number, but is not irrational
The correct answer is 4- All of the above.
Irrational numbers cannot be expressed as fractions or ratios of integers. They are non-terminating decimals, which means they have an infinite number of decimal places without repeating patterns. Additionally, irrational numbers include radicals (such as the square root of 2 or pi) that cannot be simplified to whole numbers. Therefore, all of the given options are characteristics of irrational numbers.
The correct answer is 4- All of the above.
To understand why the answer is 4, let's break down each option:
1- Irrational numbers are not fractions: This is true. An irrational number cannot be expressed as the ratio of two integers. This means that it cannot be written in the form of a/b, where a and b are integers.
2- Irrational numbers are non-terminating and non-repeating decimals: This is also true. Unlike rational numbers, which can be expressed exactly as decimals that either terminate (end) or repeat, irrational numbers have decimal representations that go on forever without showing a clear pattern. For example, the square root of 2 (√2) is an irrational number, and its decimal representation is approximately 1.41421356... It goes on indefinitely without repeating.
3- Irrational numbers can be radicals that do not simplify to whole numbers: This is also true. Some irrational numbers can be expressed as radicals, such as the square root of 2 (√2) or the cube root of 5 (∛5), but these radicals cannot be simplified to whole numbers or a ratio of integers.
Since all three statements (non-fractions, non-terminating and non-repeating decimals, radicals that do not simplify to whole numbers) are true about irrational numbers, the correct answer is 4- All of the above.