How do you simplify $\sqrt{50} - \sqrt{18} ?$ $sqrt(50) - sqrt(18)?$

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Answer 1 · 2018-06-11T19:21:00

$2 \sqrt{2}$ $2sqrt2$

The key realization here is that we can leverage the radical property

$\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab)=sqrtasqrtb$

Thus, we can rewrite $\sqrt{50} - \sqrt{18}$ $color(blue)(sqrt50)-color(red)(sqrt18)$ as

$\sqrt{25 \cdot 2} - \sqrt{9 \cdot 2}$ $color(blue)(sqrt(25*2))-color(red)(sqrt(9*2))$

which simplifies to

$5 \sqrt{2} - 3 \sqrt{2}$ $5sqrt2-3sqrt2$

Factoring out a $\sqrt{2}$ $sqrt2$ , we get

$\sqrt{2} (5 - 3)$ $sqrt2(5-3)$

Which simplifies to

$2 \sqrt{2}$ $2sqrt2$

Hope this helps!

How do you simplify sqrt(50) - sqrt(18)?√50−√18?sqrt(50) - sqrt(18)?