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General

Easy

Question

# Classify whether the following Surd is rational or irrational , justify 8-√48

Hint:

### Use properties of rational and irrational numbers.

## The correct answer is: irrational number.

### Complete step by step solution:

On prime factorization, we can write

(It is an irrational number)

(It is a rational number)

Here one number is irrational and the other is rational.

On subtraction, we have , we get an irrational number.

(Since rational number - irrational number = irrational number)

This cant be written in the form , where p and q are integers.

∴ is an irrational number.

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