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Maths-

General

Easy

Question

Classify whether the following Surd is rational or irrational , Justify.√47+√8

hint 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
$square root of 47 equals square root of 1 cross times 47 end root$ (Since 47 is a prime number)
$square root of 8 equals square root of 2 cross times 2 cross times 2 end root equals 2 square root of 2$
Here both the numbers are irrational.
On adding $square root of 47 plus 2 square root of 2$ , we get an irrational number.
This cant be written in the form $p over q$ , where p and q are integers.
∴ $square root of 47 plus square root of 8$ is an irrational number.

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