Question

Every surd is
(a) A natural number
(b) An irrational number
(c) A whole number
(d) A rational number

Answer 1

Hint: In this question, we need to tell what type of number a surd is and we have options of natural numbers, irrational numbers, whole numbers, rational numbers. For this, we will understand the meaning of surds and then take an example to understand more clearly. At last, we will tell what every surd is.

Complete step-by-step answer:
Let us understand the definition of surds along with an example. Surds are roots \[\left( \sqrt{{}} \right)\] of numbers that cannot be simplified into a rational number. It cannot be accurately represented in a fraction. Basically, we can say that a surd is an irrational root of a rational number. Example: A square has an area of 3 sq.m. We need to find the exact length of the side of the square. As we know, \[{{\left( \text{side} \right)}^{2}}=\text{ Area}\text{.}\] So, we get,
\[\Rightarrow {{\left( \text{side} \right)}^{2}}=3\]
\[\Rightarrow \text{side}=\sqrt{3}\]
This answer is in surd form because 3 is a rational number but \[\sqrt{3}\] is an irrational number and cannot be simplified further. To find the exact answer, we should leave the answer in surd form only. \[\sqrt{2}\] is also an example of surd. Also, the cube root of 9 is a surd. Hence, from all this information, we can see that every surd is an irrational number.

So, the correct answer is “Option (b)”.

Note: Students should not square root or cube root which cannot be simplified further are called surds. They should note that \[\sqrt{\pi }\] is not a surd even though \[\sqrt{\pi }\] is irrational because \[\pi \] is not rational. Hence, we can say that every surd is an irrational number but every irrational number need not be surds.