Question

$\bf \: {Simplify \: \: \: 4 \sqrt{2} - 2 \sqrt{8} + \frac{3}{ \sqrt{2} } \: \: .}$
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Answer 1

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$\bf \scriptsize{As \: the \: given \: Irrational \: numbers \: are \: not \: similar \: , so \: we \: reduce } \\ \bf \scriptsize{\: each \: irrational \: number \: in \: simplest \: form. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\bf \scriptsize{ \: \: 2 \sqrt{8} = 2 \sqrt{2^{2} \times 2} \: = \: 2 \times \sqrt{2^{2} } \times \sqrt{2} \: = \: 2 \times 2 \: \times \sqrt{2} } \\ \\ \bf \scriptsize{ = 4 \sqrt{2} }$

$\bf \scriptsize{And \: \: \: \: \: \: \: \: \frac{ \: \: 3}{ \sqrt{6} } = \frac{ \: \: 3}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{3}{2} \sqrt{2} }$

$\bf \scriptsize{Here, \: \: \: 4 \sqrt{2} - 2 \sqrt{8} + \frac{ \: \: 3}{ \sqrt{2} } \sqrt{2} } \\ \\ \bf \scriptsize{ = \sqrt{2} \: \: (4 - 4 + \frac{3}{2} )} \\ \\ \bf \scriptsize{ = \frac{3}{2} \sqrt{2} }$

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Answer 2

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$\bf \scriptsize{As \: the \: given \: Irrational \: numbers \: are \: not \: similar \: , so \: we \: reduce } \\ \bf \scriptsize{\: each \: irrational \: number \: in \: simplest \: form. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\bf \scriptsize{ \: \: 2 \sqrt{8} = 2 \sqrt{2^{2} \times 2} \: = \: 2 \times \sqrt{2^{2} } \times \sqrt{2} \: = \: 2 \times 2 \: \times \sqrt{2} } \\ \\ \bf \scriptsize{ = 4 \sqrt{2} }$

$\bf \scriptsize{And \: \: \: \: \: \: \: \: \frac{ \: \: 3}{ \sqrt{6} } = \frac{ \: \: 3}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{3}{2} \sqrt{2} }$

$\bf \scriptsize{Here, \: \: \: 4 \sqrt{2} - 2 \sqrt{8} + \frac{ \: \: 3}{ \sqrt{2} } \sqrt{2} } \\ \\ \bf \scriptsize{ = \sqrt{2} \: \: (4 - 4 + \frac{3}{2} )} \\ \\ \bf \scriptsize{ = \frac{3}{2} \sqrt{2} }$