Irrational Numbers

4.8

-52 is a rational number because it can be expressed as a fraction in the form of -52/1

rational

Well, honey, the square root of zero is actually just zero. And guess what? Zero is as rational as it gets in the number world. So, yes, the square root of zero is a rational number. But hey, don't sweat it if math isn't your thing, we can't all be numbers wizards.

Oh, dude, that number is rational. It might have a bunch of repeating decimals, but hey, it can still be written as a fraction. So, like, it's totally chill in the world of rational numbers.

The number 75.082106 with a repeating decimal is rational. A rational number can be expressed as a fraction of two integers, where the denominator is not zero. In this case, the repeating decimal can be written as a fraction, making it a rational number. Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.

The number 0.424242... is rational. A rational number is one that can be expressed as a ratio of two integers, where the denominator is not zero. In this case, the repeating decimal 0.424242... can be expressed as the fraction 14/33, making it a rational number.

Well, isn't that a happy little question! 0.21 is a rational number because it can be expressed as a fraction, specifically 21/100. Just like painting a beautiful landscape, math can be a lovely and calming experience once you understand its gentle rhythms.

An irrational number is a real number that cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers. These numbers have non-repeating, non-terminating decimal representations. Examples of irrational numbers include the square root of 2, pi, and the golden ratio. They are contrasted with rational numbers, which can be expressed as fractions.

Actually, a repeating decimal is not necessarily an irrational number. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. While some repeating decimals can be irrational, such as 0.1010010001..., others can be rational, like 0.3333... which is equal to 1/3. Irrational numbers are numbers that cannot be expressed as a simple fraction, and they have non-repeating, non-terminating decimal representations.

I would say no, it is rational. A number is only irrational if it repeats with no specific pattern.

No. 2 + sqrt(5) and 2 - sqrt(2) are both irrational but their sum, 4 is rational.

The number 2468 is a rational number. A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. In this case, 2468 can be expressed as the ratio 2468/1, which makes it a rational number.

Irrational numbers are denoted by the symbol "s" to distinguish them from rational numbers, which can be expressed as fractions. Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. The symbol "s" serves as a placeholder to represent these numbers in mathematical equations and calculations.

Oh, dude, the square root of 25 is 5, which is a whole number and can be expressed as a fraction 5/1. So, yes, it is a rational number because it can be written as a ratio of two integers. But hey, who really cares about all that math stuff anyway, right?

The square root of the square root of the square root of something is called the 8th root. The 8th root of pi is approximately 1.15383506784999.

irrational

No. Irrational numbers can not be expressed as a ratio between two integers.

7.5

rational

It is a rational number because it can be expressed as a fraction

To prove that if (r) is rational and (x) is irrational, then both (rx) and (\frac{r}{x}) are rational, we can use the fact that the product or quotient of a rational and an irrational number is always irrational. Since (r) is rational and (x) is irrational, their product (rx) must be irrational. Similarly, the quotient (\frac{r}{x}) must also be irrational. Therefore, we cannot prove that both (rx) and (\frac{r}{x}) are rational based on the given information.

The square root of 79 is approximately 8.89. Rounding to the nearest whole number, the approximate square root of 79 is 9.

Rational , because it can be converted to an ratio/fraction

0.4744 = 0.4744/1.0000 = 4744/10000

Cancel down by '2'

4744/10000 = 2372/5000

Cancel down again by '2'

1186/2500

Cancel down again by '2'

593/1250 Done!!!!

NB An IRRATIONAL number is one were the decinals go to infinity AND there is NO regular order in the decimal digits.

pi = 3.141592.... Is the most well known irrational number.

However,

1/3 = 0.3333.... is NOT irrational because the decimal digits are in a regular order of '3'.

'-3' is RATIONAL.

IRRATIONAL numbers are those where the decimals go to inifinity AND there is no regular order in the decimal digits.

e.g.

pi = 3.141592..... is IRRATIONAL

but

1/3 = 0.3333.... is RATIONAL.

NB Both go to infinity, but '1/3' has the decimals in a regular order .