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प्रश्न
State with reason, whether the following is a surd and which is not?
`3sqrt(2) - 7`
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उत्तर
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.
