Question

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

`3sqrt(2) - 7`

Answer 1

Surd

Reason:

Given: `3sqrt(2) - 7`

Step-wise calculation:

1. Identify the type of terms:

`3sqrt(2)` is a term with a surd (irrational root), since `sqrt(2)` is irrational.

–7 is a rational number.

2. What is a surd?

A surd is an irrational number that can be expressed as a root of a positive rational number which is not a perfect square or perfect power for higher roots.

For example, `sqrt(2)` is a surd because it is irrational.

3. Is `3sqrt(2) - 7` a surd?

Since it contains the term `3sqrt(2)`, which is irrational (a surd) and –7 is rational, their combination remains irrational unless the rational number cancels the irrational part which it doesn’t here.

Hence, the expression `3sqrt(2) - 7` is irrational and hence a surd.

`3sqrt(2) - 7` is a surd because it contains the irrational term `3sqrt(2)` and the entire expression is irrational. It is not a rational number, so it qualifies as a surd.