Question

State which of the following are pure surds and mixed surds:
$\sqrt {21} $.
A. Pure surd
B. Mixed surd
C. Not a surd
D. None of the above

Answer 1

Hint – In order to solve this problem you should know that a surd is an expression that includes a square root, cube root or other root symbol. Surds are used to write irrational numbers precisely.

Complete step by step answer:
As we know 21 = 7x3.

A surd in which the whole of the rational number is under the radical sign and makes the radicand, is called pure surd.

In other words a surd having no rational factor except unity is called a pure surd or complete surd.

Thus, $\sqrt {21} $ is a pure surd.

Note – Surds are used to write irrational numbers precisely – because the decimals of irrational numbers do not terminate or recur, they cannot be written exactly in decimal form.

For example,
If the square has an area of $3 m^2$. Write down the exact length of the side of the square.
The length of the side is √3 m.
This answer is in surd form. It is irrational and it is said to be "in exact form". A decimal answer, such as 1.73 (2 decimal places), is not exact. Even 1.732050807568877 is not exact. When an answer is required in exact form, you must write it as a surd, ideally simplifying it if possible.