How do you simplify $32 \div (6 - 2 \sqrt{5})$ $32div(6-2sqrt5)$ ?

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How do you simplify $32 \div (6 - 2 \sqrt{5})$ $32div(6-2sqrt5)$ ?

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Answer 1 · 2018-05-08T09:33:15

$12 + 4 \sqrt{5}$ $12+4sqrt5$

Explanation:

$32 \div (6 - 2 \sqrt{5})$ $32÷(6-2sqrt5)$

means

$\frac{32}{6 - 2 \sqrt{5}}$ $32/(6-2sqrt5)$

multiply by the conjugate

$\frac{32}{6 - 2 \sqrt{5}} \cdot \frac{6 + 2 \sqrt{5}}{6 + 2 \sqrt{5}}$ $32/(6-2sqrt5)*(6+2sqrt5)/(6+2sqrt5)$

$(6 - 2 \sqrt{5}) \cdot (6 + 2 \sqrt{5}) = 6^{2} - {(2 \sqrt{5})}^{2} = 36 - 20 = 16$ $color(red)((6-2sqrt5)*(6+2sqrt5) = 6^2 - (2sqrt5)^2=36-20 = 16)$

$difference of two sequares$ $color(red)("difference of two sequares")$

$\frac{32 \cdot (6 + 2 \sqrt{5})}{16}$ $(32*(6+2sqrt5))/ 16$

$\frac{32}{16} = 2$ $color(red)(32/16 = 2)$

$2 \cdot (6 + 2 \sqrt{5}) = 12 + 4 \sqrt{5}$ $2*(6+2sqrt5) = 12+4sqrt5$

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How do you simplify $32 \div (6 - 2 \sqrt{5})$ $32div(6-2sqrt5)$ ?

1 Answer

Explanation:

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How do you simplify 32div(6-2sqrt5)32÷(6−2√5) 32div(6-2sqrt5)?

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How do you simplify $32 \div (6 - 2 \sqrt{5})$ $32div(6-2sqrt5)$ ?