Mathematics, 19.08.2020 20:01, supreme18

I need help with rational and irrational numbers here is the question. Select all true statements about the square root of 2.

-It is a real number.
-It is an irrational number.
-It is a rational number.
-It is an integer.
-It is not a real number.

Answers: 2

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Answers

answered: jraemier5861

The correct answer choices are:

1) It is a real number

2) It is an irrational number

Step-by-step explanation:

So we have the number:

$\sqrt2$

First, let's define each of the terms:

Real numbers are all of the irrational and rational numbers. If a number is irrational or rational, then they are a real number. Any number that does not include the imaginary number i is real (you'll learn this eventually. It's actually really interesting!).

Irrational numbers are the numbers that do not terminate nor repeat. Examples include π or √3. Note that numbers like 1/3 which is .3333 is not irrational because they are repeating. π, on the other hand, does not repeat and never ends.

Rational numbers are the numbers that terminate or repeat. They also include the integers, whole numbers, and natural numbers.

So, the √2. First, it's real because it doesn't deal with imaginaries.

Next, use a calculator and calculate √2. We can see that it is about 1.41423562... This number does not repeat. And it does not terminate (end). In other words, √2 is a irrational numbers.

Since it is irrational, it cannot be rational. Since it's not rational, it cannot be an integer, whole number, or a natural number.

Therefore, the correct answer choices are:

1) It is a real number

2) It is an irrational number

answered: Vyflores2528

$\Large \boxed{\mathrm{It \ is \ a \ real \ number.}} \\ \\ \Large \boxed{\mathrm{It \ is \ an \ irrational \ number.}}$