How do you simplify $\sqrt{288}$ $sqrt288$ ?

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How do you simplify $\sqrt{288}$ $sqrt288$ ?

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Answer 1 · 2015-05-23T12:11:12

You can factor the number inside the root:

$\sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3}$ $sqrt(2*2*2*2*2*3*3)$

However, $2 \cdot 2 \cdot 3 = 12$ $2*2*3=12$

Then, you have $\sqrt{2 \cdot 12 \cdot 12} = \sqrt{2 \cdot 12^{2}}$ $sqrt(2*12*12)=sqrt(2*12^2)$ .

By definition, when you have a squared number inside the square root, you can take its root out:

final answer: $12 \sqrt{2}$ $12sqrt(2)$

Answer 2 · 2015-05-23T12:15:39

In order to simplify $\sqrt{288}$ $sqrt(288)$ factor $288$ $288$ and look for pairs of factors

$288$ $288$
$= 2 \times 144$ $= 2xx144$
$= 2 \times 12 \times 12$ $= 2xxcolor(red)( 12) xx color(red)(12)$
and therefore
$\sqrt{288} = \sqrt{2 \times 12^{2}} = 12 \sqrt{2}$ $sqrt(288) = sqrt(2xx12^2) = 12sqrt(2)$

If you did not recognize $144$ $144$ as $12^{2}$ $12^2$ you could have continued the factoring as
$2 \times 144$ $2xx144$
$= 2 \times 2 \times 72$ $=2xx2xx72$
$= 2 \times 2 \times 2 \times 36$ $=2xx2xx2xx36$
$= 2 \times 2 \times 2 \times 2 \times 18$ $=2xx2xx2xx2xx18$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 9$ $=2xx2xx2xx2xx2xx9$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$ $=2xx2xx2xx2xx2xx3xx3$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$ $=color(red)(2)xxcolor(red)(2)xxcolor(blue)(2)xxcolor(blue)(2)xx2xxcolor(orange)(3)xxcolor(orange)(3)$
So
$\sqrt{288} = \sqrt{2^{2} \cdot 2^{2} \cdot 2 \cdot 3^{2}}$ $sqrt(288) = sqrt(color(red)(2^2)*color(blue)(2^2)*2*color(orange)(3^2))$
$= 2 \cdot 2 \cdot 3 \sqrt{2}$ $= color(red)(2)*color(blue)(2)*color(orange)(3)sqrt(2)$
$= 12 \sqrt{2}$ $=12sqrt(2)$

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How do you simplify $\sqrt{288}$ $sqrt288$ ?

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