Question

$(3 + \sqrt{3)} (2 + \sqrt{2)}$
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Answer 1

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Answer 2

AnswEr-:

• $\:\:\:\:\:\:\:\:\:\red{\underline {\boxed{\mathrm { Answer \:-: 6 + \sqrt[3] {2}+ \sqrt[2]{3} + \sqrt {6}}}}}$

Explanation-:

• $\implies{\mathrm {Simplify \:-:\bf{ (3 + \sqrt{3)} (2 + \sqrt{2})}}}$

$\dag{\mathrm {\bf{Solution \:of\:Question \:-:}}}$

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• $\implies{\mathrm {Simplify \:-:\bf{ (3 + \sqrt{3)} (2 + \sqrt{2})}}}$

Now Simplifying the Expression -:

• $\implies{\mathrm {Simplify \:-:\bf{ (3 + \sqrt{3)} (2 + \sqrt{2})}}}$

• $\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\mathrm { (3 + \sqrt{3)} (2 + \sqrt{2})}}$

• $\mathrm { \star{ By \: Multiplying \: each \:term\:-:}}$

• $\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\mathrm { \purple{(3 + \sqrt{3})} (2 + \sqrt{2})}}$

• $\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\mathrm { \purple {3}(2 +\sqrt {2})\purple {+ \sqrt{3}} (2 + \sqrt{2})}}$

• $\:\:\:\:\:\:\:\:\::\implies{\mathrm { \purple {3(2 +\sqrt {2})}+ \sqrt{3} (2 + \sqrt{2})}}$

• $\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\mathrm { \purple {3 \times 2 +3 \times \sqrt {2}}+ \sqrt{3} (2 + \sqrt{2})}}$

• $\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\mathrm { 3 \times 2 +3 \times \sqrt {2}\purple{+ \sqrt{3} (2 + \sqrt{2})}}}$

• $\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\mathrm { 3 \times 2 +3 \times \sqrt {2}\purple{+ \sqrt{3} \times 2 + \sqrt {3}\times \sqrt{2}}}}$

• $\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\mathrm { \purple {6 + \sqrt[3] {2}+ \sqrt[2]{3} + \sqrt {6}}}}$

Hence ,

• $\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\red{\underline {\boxed{\mathrm { Answer \:-: 6 + \sqrt[3] {2}+ \sqrt[2]{3} + \sqrt {6}}}}}$

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