How do you simplify $\sqrt{50} + \sqrt{32} - \sqrt{8}$ $sqrt50+sqrt32-sqrt8$ ?

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How do you simplify $\sqrt{50} + \sqrt{32} - \sqrt{8}$ $sqrt50+sqrt32-sqrt8$ ?

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Answer 1 · 2017-03-20T00:20:27

$\sqrt{50} + \sqrt{32} - \sqrt{8} = 7 \sqrt{2}$ $sqrt(50)+sqrt(32)-sqrt(8)=color(purple)(7sqrt2$

Explanation:

Simplify:

$\sqrt{50} + \sqrt{32} - \sqrt{8}$ $sqrt(50)+sqrt(32)-sqrt(8)$

Terms with square roots can be added or subtracted only if their square roots are the same. Therefore, we need to simplify each term by prime factorization.

$\sqrt{50} = \sqrt{2 \times (5 \times 5)} = 5 \sqrt{2}$ $color(red)(sqrt(50)=sqrt(2xx(5xx5))=5sqrt(2)$

$\sqrt{32} = \sqrt{(2 \times 2) \times (2 \times 2) \times 2} = 4 \sqrt{2}$ $color(blue)(sqrt(32)=sqrt((2xx2)xx(2xx2)xx2)=4sqrt(2)$

$\sqrt{8} = \sqrt{(2 \times 2) \times 2} = 2 \sqrt{2}$ $color(green)(sqrt(8)=sqrt((2xx2)xx2)=2sqrt(2)$

All terms now have the same square root and can now be added or subtracted.

$5 \sqrt{2} + 4 \sqrt{2} - 2 \sqrt{2}$ $color(red)(5sqrt2) + color(blue)(4sqrt2) - color(green)(2sqrt2)$

Simplify.

$7 \sqrt{2}$ $color(purple)(7sqrt2$

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How do you simplify $\sqrt{50} + \sqrt{32} - \sqrt{8}$ $sqrt50+sqrt32-sqrt8$ ?

1 Answer

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How do you simplify sqrt50+sqrt32-sqrt8√50+√32−√8sqrt50+sqrt32-sqrt8?

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How do you simplify $\sqrt{50} + \sqrt{32} - \sqrt{8}$ $sqrt50+sqrt32-sqrt8$ ?