Question

Rationalize the denominator : 3+√2/4√2.
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Answer 1

SoluTion:

Given expression : $\sf{\dfrac{3\:+\:\sqrt{2}}{4\:\sqrt{2}}}$

We've to rationalize it,

For rationalize it, Multiply and divide the given expression with 4√2.

: $\implies$  $\sf{\dfrac{3\:+\:\sqrt{2}}{4\:\sqrt{2}}}$  $\sf{\times\:\dfrac{4 \sqrt{2}}{4 \sqrt{2}}}$

: $\implies$ $\sf{\dfrac{(3\:+\:\sqrt{2})(4 \sqrt{2})}{(4 \sqrt{2})^2}}$

: $\implies$ $\sf{\dfrac{12 \sqrt{2} \:+\:4 \times 2}{16 \times 2}}$

: $\implies$ $\sf{\dfrac{12 \sqrt{2} \:+\:8}{32}}$

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: $\implies$ $\large{\boxed{\sf{\dfrac{3 \sqrt{2}\:+\:2}{8}}}}$

Answer 2

$\frac{3 + 2 \sqrt{2} }{4 \sqrt{2} } \\ \\ = \frac{(3 + 4 \sqrt{2})(4 \sqrt{2} )}{4 \sqrt{2} \times 4 \sqrt{2} } \\ \\ = \frac{12 \sqrt{2} + 8 }{32} \\ \\ = \dfrac{2 + 3 \sqrt{2} }{8}$