How do you simplify $(8+sqrt48)/4$ ?

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Answer 1 · 2017-04-12T07:22:29

$2+sqrt(3)$

Simplify your radical (square root):

To simplify a square root, use perfect squares such as
$2^2 = 4$
$3^2 = 9$
$4^2 = 16$
$sqrt(48) = sqrt(16*3)$

Use the rule that says $sqrt(m*n) = sqrt(m)sqrt(n)$

$sqrt(48) = sqrt(16) sqrt(3) = 4 sqrt(3)$

So $(8 + sqrt(48))/4 = (8 + 4 sqrt(3))/4$

Factor a 4 from each number in the numerator:

$(8 + 4 sqrt(3))/4 = (4(2+sqrt(3)))/4$

Cancel the 4's because $4/4 = 1$

So $(8 + sqrt(48))/4 = (8 + 4 sqrt(3))/4 = (4(2+sqrt(3)))/4 = 2+sqrt(3)$

How do you simplify (8+sqrt48)/4(8+sqrt48)/4?