How do you simplify $sqrt8(5 sqrt 2 - sqrt 18)$ ?

Question

1842 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-24T05:09:47

First, notice that $sqrt8 = sqrt(4*2) = 2sqrt2$

Also, notice that $sqrt18 = sqrt(9*2) = 3sqrt2$

Now we have $2sqrt2(5sqrt2 - 3sqrt2)$

We can just subtract inside the parenthesis

Treating the radicals as variables, just subtract and get $2sqrt2$

Now we have $2sqrt2 * 2sqrt2$

We just multiply the radicals with radicals and integers with integers

$2*2 = 4$
$sqrt2 * sqrt2 = sqrt2^2 = 2$

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

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