Question

Which of the following is surd ? Choose the correct option.
A.\[\sqrt{17}\]
B. \[\sqrt{4}\]
C. \[2\]
D. \[3\]

Answer 1

Hint: The surds are the numbers that are in the roots and are also irrational numbers. So check for the numbers that can’t be simplified further and are in roots after simplification.

Complete step-by-step answer:
In the question, we have to check which number is a surd.
Now, we know that the number that is in roots after simplification is a surd.
Also, the surds are irrational numbers in its root form. So we will start with the first option that is \[\sqrt{17}\], now this number can’t be further simplified and hence this is a surd.
Next, we take the second number\[\sqrt{4}\], which can also be simplified as\[\sqrt{4}\,=2\], so we get a whole number and hence \[\sqrt{4}\] is not a surd. Similarly, 2 and 3 are also not surds.
Hence the only number that is a surd is \[\sqrt{17}\]. So the correct answer is option A.

Note: Not all numbers in the roots are called surd. For example \[\sqrt{4}\,,\,\sqrt{9}\,,\sqrt{16}\,\]are not surds, because\[\sqrt{4}\,=2,\,\sqrt{9}\,=3,\sqrt{16}=4\,\], so we get all the whole numbers after simplifying each roots.