Question

Simplify (³√3+²√2)(²√3+³√2)​

Answer 1

Solution!!

$\sf \to (\sqrt[3]{3}+\sqrt{2})(\sqrt{3}+\sqrt[3]{2})$

Multiply the parentheses.

$\sf \to \sqrt[3]{3}\sqrt{3}+\sqrt[3]{6}+\sqrt{6}+\sqrt{2}\sqrt[3]{2}$

Use $\sf \sqrt[n]{a}=\sqrt[mn]{a^{m}}$ to expand the expression.

$\sf \to \sqrt[6]{3^{2}}\sqrt[6]{3^{3}}+\sqrt[3]{6}+\sqrt{6}+\sqrt[6]{2^{3}}\sqrt[6]{2^{2}}$

The product of roots with the same index is equal to the root of the product.

$\sf \to \sqrt[6]{3^{2}\times 3^{3}}+\sqrt[3]{6}+\sqrt{6}+\sqrt[6]{2^{3}\times 2^{2}}$

Use $\sf a^{m}\times a^{n}=a^{m+n}$ to calculate the product.

$\sf \to \sqrt[6]{3^{5}}+\sqrt[3]{6}+\sqrt{6}+\sqrt[6]{2^{5}}$

Evaluate the power.

$\sf \to \sqrt[6]{243}+\sqrt[3]{6}+\sqrt{6}+\sqrt[6]{32}$