How do you simplify $sqrt3*sqrt27$ ?

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Answer 1 · 2016-06-13T03:09:10

$= 9$

$sqrt3 * sqrt27$

$sqrt27$ can be simplified by prime factorisation. (expressing a number as a product of its prime factors)

$sqrt27= sqrt ( 3 * 3 * 3 ) = sqrt (3 * 3^2) = color(blue)(3sqrt3$

The expression can now be written as:
$sqrt3 * sqrt27 = sqrt 3 * color(blue)(3sqrt3$

$= 3 * sqrt 3 * color(blue)(sqrt3$

$= 3 * 3$

$= 9$

Answer 2 · 2016-06-14T20:28:17

= $sqrt81 = 9$

When multiplying or dividing with roots, two roots can be combined into one root.

$sqrt3 xx sqrt 27 = sqrt(3 xx27)$

= $sqrt81$

$=9$

How do you simplify sqrt3*sqrt27sqrt3*sqrt27?