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Identities for Irrational Numbers

The simplifie...

Question

The simplified value of $(\sqrt{2} + 1) (\sqrt{3} + \sqrt{2}) (\sqrt{8} - 2) (\sqrt{12} + \sqrt{8})$ is

A

3

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B

4

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C

2

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D

1

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Solution

The correct option is B 4
$(\sqrt{2} + 1) (\sqrt{3} + \sqrt{2}) (\sqrt{8} - 2) (\sqrt{12} - \sqrt{8})$
= $(\sqrt{2} + 1) (\sqrt{3} + \sqrt{2}) [2 (\sqrt{2} - 1)] [2 (\sqrt{3} - \sqrt{2})]$
= $4 (\sqrt{2} + 1) (\sqrt{3} + \sqrt{2}) (\sqrt{2} - 1) (\sqrt{3} - \sqrt{2})$
= $4 (2 - 1) (3 - 2) = 4$

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