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Distribute 7sqrt(6) to each term inside the parentheses.

Mathematics

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Answer

2815−70328\sqrt{15} - 70\sqrt{3}

Step-by-step solution

5 steps

Here's the solution for question 8.

8. Calculate the product: 76(210−52)7\sqrt{6}(2\sqrt{10} - 5\sqrt{2})

  1. Distribute 767\sqrt{6} to each term inside the parentheses.

    76⋅(210)−76⋅(52)7\sqrt{6} \cdot (2\sqrt{10}) - 7\sqrt{6} \cdot (5\sqrt{2})

  2. Multiply the coefficients and the terms under the square roots for each part.

    (7⋅2)6⋅10−(7⋅5)6⋅2(7 \cdot 2)\sqrt{6 \cdot 10} - (7 \cdot 5)\sqrt{6 \cdot 2} 1460−351214\sqrt{60} - 35\sqrt{12}

  3. Simplify the surds 60\sqrt{60} and 12\sqrt{12}.

    60=4⋅15=4⋅15=215\sqrt{60} = \sqrt{4 \cdot 15} = \sqrt{4} \cdot \sqrt{15} = 2\sqrt{15} 12=4⋅3=4⋅3=23\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}

  4. Substitute the simplified surds back into the expression.

    14(215)−35(23)14(2\sqrt{15}) - 35(2\sqrt{3})

  5. Perform the final multiplications.

    2815−70328\sqrt{15} - 70\sqrt{3}

    The terms 15\sqrt{15} and 3\sqrt{3} are not like terms, so they cannot be combined further.

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