Question

Find the value of :- $(\sqrt{3}+\sqrt{2}{)}^6(\sqrt{3}-\sqrt{2}{)}^6$ = ?

Answer 1

We have,

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

$={\left[(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})\right]}^6$

$={[{\left(\sqrt{3}\right)}^2-{\left(\sqrt{2}\right)}^2]}^6$

$={[3-2]}^6$

$=1^6$

$=1$

Hence, this is the answer.