Verified Answer :

The set of numbers \(\sqrt{51}\) belongs to is termed as B. irrational numbers.

There are two main types of numbers, real and imaginary. Real numbers are also subdivided into rational and irrational numbers. Irrational numbers are numbers that cannot be written in a fractional form which is the opposite of rational numbers. These can either be non-terminating or repeating. An example of a non-terminating irrational number is the value of pi (3.1415...) and an example of a repeating irrational number is 15.55555...

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Answer:

B


Step-by-step explanation:


Natural Numbers are {1, 2, 3, 4, ..... 100, 101, 102, .....}

Integers are ALL the natural numbers and their negative counterparts as well as 0.

  • Integers are {... -102, -101, -100, .... -4, -3, -2, -1, 0, 1, 2, 3, 4, .... 100, 101, 102, ...}

Rational Numbers are numbers that can be written as a fraction.

  • Examples are 1, 2, \(\frac{1}{3}\) , \(-\frac{5}{12}\)  ... etc.

Irrational Numbers are the ones that CANNOT be written as fractions.

  • Examples are  \(\sqrt{2} , \sqrt{7} , \sqrt{31} ,  \pi\) , etc.

So our number \(\sqrt{51}\) CANNOT BE written as a fraction. So it is an Irrational Number. Answer choice B is correct.

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