(√3+√2)^6 (√3+√2)^6 ( ( √ #160; 3 +√ #160; 2 #160; ) #160; ^ 3 ) #160; ^ 2 ( ( √ #160; 3 +√ #160; 2 #160; ) #160; ^ 3 ) ...

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Operations on Rational and Irrational Numbers

Solve : √3+√...

Question

Solve :
$(\sqrt{3} + \sqrt{2})^{6} - (\sqrt{3} - \sqrt{2})^{6}$

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Solution

${(\sqrt 3 + \sqrt 2)}^{6} - {(\sqrt 3 + \sqrt 2)}^{6}$
${({(\sqrt 3 + \sqrt 2)}^{3})}^{2} - {({(\sqrt 3 + \sqrt 2)}^{3})}^{2}$
$({(\sqrt 3 + \sqrt 2)}^{3} - {(\sqrt 3 + \sqrt 2)}^{3}) + ({(\sqrt 3 + \sqrt 2)}^{3} - {(\sqrt 3 + \sqrt 2)}^{3})$
$[3 \sqrt 3 + 2 \sqrt 2 + 3 \sqrt 56 (\sqrt 3 + \sqrt 2) - (3 \sqrt 3 + 2 \sqrt 2 + 3 \sqrt 6 (\sqrt 3 - \sqrt 2))]$
$[3 \sqrt 3 + 2 \sqrt 2 + 3 \sqrt 6 (\sqrt 3 + \sqrt 2) + (3 \sqrt 3 + 2 \sqrt 2 + 3 \sqrt 6 (\sqrt 3 - \sqrt 2))]$
$[3 \sqrt 3 + 2 \sqrt 2 + 3 \sqrt 6 (\sqrt 3 + \sqrt 2) + (3 \sqrt 3 + 2 \sqrt 2 + 3 \sqrt 6 (\sqrt 3 - \sqrt 2))]$
$[3 \sqrt 3 + 2 \sqrt 2 + 3 \sqrt 6 (\sqrt 3 + \sqrt 2) + (3 \sqrt 3 - 2 \sqrt 2 - 3 \sqrt 6 (\sqrt 3 - \sqrt 2))]$
$[4 \sqrt 2 + 5 \sqrt 6 (\sqrt 3 + \sqrt 2 + \sqrt 3 - \sqrt 2)] [6 \sqrt 3 + 2.6. \sqrt 3]$
$(4 \sqrt 2 + 6.3 \sqrt 2) (6 \sqrt 3 + 12 \sqrt 3)$
$(4 \sqrt 2 + 18 \sqrt 2) (6 \sqrt 3 + 12 \sqrt 3)$
$2 \sqrt 2 (2 + 9) 6 \sqrt 3 (1 + 2)$
$2 \sqrt 2 (11) 6 \sqrt 3 (3)$
$6 \times 6 \sqrt 6 \Rightarrow 396 \sqrt 6$ Ans.

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