Is 2 the same as its square root?
Number System is the system of writing numbers. A number is a value used for counting, labeling, calculating, etc. There are various types of numbers: whole numbers, natural numbers real numbers, irrational numbers, rational numbers, integers, etc.
Types of Numbers
Based on the different properties that numbers reflect and the relationship between them, numbers are classified into different sets or types. Below given are some important sets of numbers,
- Natural numbers: Natural numbers are also known as counting numbers. They are positive starting from 1 to infinity. Example: 2, 3, 4 etc.
- Whole numbers: are known as natural numbers along with 0. They are positive and start from 0 up to infinity.
- Integers: The positive whole numbers along with negative natural numbers make up integers. Example: -1, 2, 0 etc.
- Real numbers: They constitute integers, fractional numbers, rational numbers, irrational numbers whole numbers or decimal numbers. Example: 0.65, 6, etc.
- Rational numbers: Any number which is expressed of the form p/q where q is not equal to zero. Example: 2.
- Irrational numbers: the numbers which cannot be expressed in the form p/q. Example: √2, π, etc.
The square root of a number is the factor of a number which when multiplied by the factor itself gives the original number. The power is basically 0.5. Generally, express square roots are expressed by using √. It is helpful when we want to find the factors of large numbers. It is a function which either gives a negative or a positive root value. For example, let us find the square root of 841. The value of the root is either 29 or -29.
One can find square roots by prime factorization method, repeated subtraction method, estimation method, and long division method. When the square root of complex numbers is found, it gives us complex numbers.
Is 2 the same as square root?
The answer is No. The square root of 2 is 1.414… √2 is an irrational number as it cannot be expressed in the form of p/q and has an infinite number of decimals. On the other hand, 2 is rational since it can be expressed in the form of 2/1 where 1 is not equal to zero.
Question 1: Is √4 irrational?
No. The square root of √4 is 2 and -2 which are rational.
Question 2: Do rational and irrational numbers belong to the class of real numbers?
Yes, rational and irrational numbers belong to a class of real numbers. Real numbers constitute integers, fractional numbers, rational numbers, irrational numbers whole numbers, or decimal numbers.
Question 3: Is 3.333333333333333… irrational?
Yes. Since it cannot be expressed of the form p/q and is recurring that is it has infinite decimals.
Question 4: What is the sum of a rational and an irrational number. Is the sum of 2 irrational numbers always irrational?
The sum of rational and irrational is always irrational. For example, 2 + √2 is irrational
The sum of 2 irrational numbers is not always irrational
For example, √3 + (-√3) is 0 which is rational.
Question 5: Check whether √5, π, 7√2 are rational?
No. √5, π, 7√5 are irrational as they are non-terminating, nonrepeating.