How do you simplify $root3(16 )+ 3+root3(54))$ ?

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Answer 1 · 2015-10-09T02:23:17

$5root(3)(2) + 3$

Factor 16, down to its primes

Factor 54, down to its primes

$54|2$
$27|3$
$color(white)(0)9|3$
$color(white)(0)3|3$
$color(white)(0)1|2*3^3$

Subsitute these

$root(3)(2^3*2) + 3 + root(3)(2*3^3)$

Everything with an exponent that's 3 or a multiple of it can come out of the root

$2root(3)(2) + 3 + 3root(3)(2)$

Sum everything that has $root(3)(2)$ together

$5root(3)(2) + 3$

How do you simplify root3(16 )+ 3+root3(54))root3(16 )+ 3+root3(54))?