How do you simplify #5sqrt8-4sqrt72+3sqrt96#?

Question

Autumn Arnold · Accepted Answer

#5sqrt8-4sqrt72+3sqrt96=12sqrt6-14sqrt2# #5sqrt8-4sqrt72+3sqrt96# = #5sqrt(ul(2xx2)xx2)-4sqrt(ul(2xx2)xx2xxul(3xx3))+3sqrt(ul(2xx2xx2xx2)xx2xx3)# = #5xx2xxsqrt2-4xx2xx3xxsqrt2+3xx2xx2xxsqrt(2xx3)# = #10sqrt2-24sqrt2+12sqrt6# = #12sqrt6-14sqrt2#

Mila Anderson · Answer

undefined To simplify $5\sqrt{8} - 4\sqrt{72} + 3\sqrt{96}$, first, factor the numbers under the square roots:

$$ 8 = 2 \times 2 \times 2 $$
$$ 72 = 2 \times 2 \times 2 \times 3 \times 3 $$
$$ 96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 $$

Then, simplify each square root:

$$ \sqrt{8} = \sqrt{2 \times 2 \times 2} = 2\sqrt{2} $$
$$ \sqrt{72} = \sqrt{2 \times 2 \times 2 \times 3 \times 3} = 6\sqrt{2} $$
$$ \sqrt{96} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3} = 4\sqrt{6} $$

Now, substitute these simplified square roots back into the expression:

$$ 5\sqrt{8} - 4\sqrt{72} + 3\sqrt{96} = 5(2\sqrt{2}) - 4(6\sqrt{2}) + 3(4\sqrt{6}) $$

$$ = 10\sqrt{2} - 24\sqrt{2} + 12\sqrt{6} $$

$$ = (10 - 24)\sqrt{2} + 12\sqrt{6} $$

$$ = -14\sqrt{2} + 12\sqrt{6} $$

So, $5\sqrt{8} - 4\sqrt{72} + 3\sqrt{96}$ simplifies to $-14\sqrt{2} + 12\sqrt{6}$.