Simplify ( square root of 2+ square root of 3)*( square root of 3- square root of 2)

$(\sqrt{2} + \sqrt{3}) \cdot (\sqrt{3} - \sqrt{2})$

Expand $(\sqrt{2} + \sqrt{3}) (\sqrt{3} - \sqrt{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{2 \cdot 3} + \sqrt{2} (- \sqrt{2}) + \sqrt{3} \sqrt{3} + \sqrt{3} (- \sqrt{2})$

Multiply $2$ by $3$ .

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

Multiply $\sqrt{2} (- \sqrt{2})$ .

Raise $\sqrt{2}$ to the power of $1$ .

$\sqrt{6} - ({\sqrt{2}}^{1} \sqrt{2}) + \sqrt{3} \sqrt{3} + \sqrt{3} (- \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$\sqrt{6} - ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) + \sqrt{3} \sqrt{3} + \sqrt{3} (- \sqrt{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{6} - {\sqrt{2}}^{1 + 1} + \sqrt{3} \sqrt{3} + \sqrt{3} (- \sqrt{2})$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\sqrt{6} - {(2^{\frac{1}{2}})}^{2} + \sqrt{3} \sqrt{3} + \sqrt{3} (- \sqrt{2})$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{6} - 2^{\frac{1}{2} \cdot 2} + \sqrt{3} \sqrt{3} + \sqrt{3} (- \sqrt{2})$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\sqrt{6} - 2^{1} + \sqrt{3} \sqrt{3} + \sqrt{3} (- \sqrt{2})$

Evaluate the exponent.

$\sqrt{6} - 1 \cdot 2 + \sqrt{3} \sqrt{3} + \sqrt{3} (- \sqrt{2})$

Multiply $- 1$ by $2$ .

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

Combine using the product rule for radicals.

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

Multiply $3$ by $3$ .

$\sqrt{6} - 2 + \sqrt{9} + \sqrt{3} (- \sqrt{2})$

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

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

Multiply $\sqrt{3} (- \sqrt{2})$ .

Combine using the product rule for radicals.

$\sqrt{6} - 2 + 3 - \sqrt{3 \cdot 2}$

Multiply $3$ by $2$ .

$\sqrt{6} - 2 + 3 - \sqrt{6}$

Subtract $\sqrt{6}$ from $\sqrt{6}$ .

$0 - 2 + 3$

Subtract $2$ from $0$ .

$- 2 + 3$

Add $- 2$ and $3$ .

$1$

Simplify ( square root of 2+ square root of 3)*( square root of 3- square root of 2)

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