Radicals: What are the steps to find the product of (6+√5)*(1-√ 5)?

The answer is 1-5√ 5 but I'm not sure how to get there.

Update:

After foiling 6*1 - 6*√ 5 + 1*√ 5 - √ 5√ 5

2 Answers

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  • 8 years ago
    Favorite Answer

    Use FOILing, as you said.

    The √5 * √5 actually equals 5, since 5^1/2 * 5^1/2 = 5^1 = 5

    = 6 - 6√5 + √5 - 5

    = 1 - 5√5

    ~HTH

  • JoAn
    Lv 4
    8 years ago

    use distributive property of multiplication

    distribute the first factor to the terms of the second factor

    (6+√5)(1-√5) = (6+√5)(1) - (6+√5)(√5)

    again use distributive property to evaluate (6+√5)(1) and (6+√5)(√5)

    (6+√5)(1-√ 5) = ((1)(6) + (1)(√5)) - ((√5)(6)+ (√5)(√5))

    (6+√5)(1-√ 5) = (6 + √5) - (6√5+ √5²)

    again use distributive property to distribute the negative sign

    (6+√5)(1-√ 5) = 6 + √5 - 6√5 - √5²

    (6+√5)(1-√ 5) = 6 + √5 - 6√5 - 5

    (6+√5)(1-√ 5) = 6 - 5 + √5 - 6√5

    combine like terms

    (6+√5)(1-√ 5) = 1 - (5√5) <---- answer

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