How do you simplify $\sqrt{8} (5 \sqrt{2} - \sqrt{18})$ $sqrt8(5 sqrt 2 - sqrt 18)$ ?

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Answer 1 · 2016-02-24T05:09:47

First, notice that $\sqrt{8} = \sqrt{4 \cdot 2} = 2 \sqrt{2}$ $sqrt8 = sqrt(4*2) = 2sqrt2$

Also, notice that $\sqrt{18} = \sqrt{9 \cdot 2} = 3 \sqrt{2}$ $sqrt18 = sqrt(9*2) = 3sqrt2$

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

We can just subtract inside the parenthesis

Treating the radicals as variables, just subtract and get $2 \sqrt{2}$ $2sqrt2$

Now we have $2 \sqrt{2} \cdot 2 \sqrt{2}$ $2sqrt2 * 2sqrt2$

We just multiply the radicals with radicals and integers with integers

$2 \cdot 2 = 4$ $2*2 = 4$
$\sqrt{2} \cdot \sqrt{2} = {\sqrt{2}}^{2} = 2$ $sqrt2 * sqrt2 = sqrt2^2 = 2$

And finally, just multiply to get $2 \cdot 4 = 8$ $2 * 4 = 8$

How do you simplify √8(5√2−√18)sqrt8(5 sqrt 2 - sqrt 18)?