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(3+sqrt7)(4-sqrt13)

Home w $\newline$ $(3+\sqrt{7})(4-\sqrt{13})$

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Multiply radical expressions

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Q. Home w

\newline

(3+\sqrt{7})(4-\sqrt{13})

Apply Distributive Property: First, we'll use the distributive property (FOIL method) to multiply these two binomials. $\newline$ $(3+\sqrt{7})(4-\sqrt{13}) = 3\cdot 4 + 3\cdot (-\sqrt{13}) + \sqrt{7}\cdot 4 - \sqrt{7}\cdot\sqrt{13}$
Multiply Numbers: Now, let's multiply the numbers. $\newline$ $3 \times 4 = 12$ $\newline$ $3 \times (-\sqrt{13}) = -3\sqrt{13}$ $\newline$ $\sqrt{7} \times 4 = 4\sqrt{7}$ $\newline$ $-\sqrt{7} \times \sqrt{13} = -\sqrt{7 \times 13}$
Combine Calculated Terms: Next, we combine all the terms we've calculated. $12 - 3\sqrt{13} + 4\sqrt{7} - \sqrt{7\times13}$
Simplify Last Term: We simplify the last term, $\sqrt{7\times13}$ . $-\sqrt{7\times13} = -\sqrt{91}$
Write Simplified Expression: Finally, we write down the simplified expression. $12 - 3\sqrt{13} + 4\sqrt{7} - \sqrt{91}$

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