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Home ws (3+sqrt7)(4-sqrt13)

Home ws\newline(3+7)(4−13) (3+\sqrt{7})(4-\sqrt{13})

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Full solution

Q. Home ws\newline(3+7)(4−13) (3+\sqrt{7})(4-\sqrt{13})
  1. Apply Distributive Property: First, we'll use the distributive property to multiply the two binomials.\newline(3+7)(4−13)=3⋅4+3⋅(−13)+7⋅4−7⋅13(3+\sqrt{7})(4-\sqrt{13}) = 3\cdot 4 + 3\cdot (-\sqrt{13}) + \sqrt{7}\cdot 4 - \sqrt{7}\cdot \sqrt{13}
  2. Multiply Each Term: Now, let's multiply each term. 3×4=123 \times 4 = 12, 3×(−13)=−3133 \times (-\sqrt{13}) = -3\sqrt{13}, 7×4=47\sqrt{7} \times 4 = 4\sqrt{7}, and 7×13=7×13\sqrt{7} \times \sqrt{13} = \sqrt{7 \times 13}
  3. Combine Calculated Terms: Next, we combine all the terms we calculated. 12−313+47−7×1312 - 3\sqrt{13} + 4\sqrt{7} - \sqrt{7\times13}
  4. Simplify Square Root: Simplify the square root of the product. 7×13=91\sqrt{7\times13} = \sqrt{91}
  5. Write Final Expression: Now, we write down the final simplified expression. 12−313+47−9112 - 3\sqrt{13} + 4\sqrt{7} - \sqrt{91}

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