Question

State with reason, whether the following is a surd and which is not?

`sqrt(12)`

Answer 1

Surd

Reason:

Given: `sqrt(12)`

Step wise calculation:

1. Express 12 as a product of perfect squares and other factors:

`sqrt(12) = sqrt(4 xx 3)`

= `sqrt(4) xx sqrt(3)`

= `2sqrt(3)`

2. Since `sqrt(3)` is an irrational number and cannot be simplified to a rational number, `2sqrt(3)` is also irrational.

`sqrt(12)` is a surd because it is an irrational root that cannot be expressed as a rational number.