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How do you simplify $\sqrt{54}$ $sqrt(54)$ ?

1 Answer

Jun 30, 2015

$\sqrt{54} = 3 \sqrt{6}$ $sqrt(54) = 3sqrt(6)$

Explanation:

Factor $54$ $54$ into primes:
$XXXX$ $color(white)("XXXX")$ $54 = 2 \cdot 27$ $54=2*27$
$XXXX$ $color(white)("XXXX")$ $= 2 \cdot 3 \cdot 9$ $=2*3*9$
$XXXX$ $color(white)("XXXX")$ $= 2 \cdot 3 \cdot 3 \cdot 3$ $=2*3*3*3$

Grouping pairs of identical factors:
$XXXX$ $color(white)("XXXX")$ $54 = 3^{2} \cdot 3 \cdot 2$ $54 = 3^2*3*2$
$XXXX$ $color(white)("XXXX")$ $= 3^{2} \cdot 6$ $=3^2*6$

$\sqrt{54} = \sqrt{3^{2} \cdot 6}$ $sqrt(54) = sqrt(3^2*6)$
$XXXX$ $color(white)("XXXX")$ $= \sqrt{3^{2}} \cdot \sqrt{6}$ $=sqrt(3^2)*sqrt(6)$

$XXXX$ $color(white)("XXXX")$ $= 3 \sqrt{6}$ $=3sqrt(6)$

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