## Algebra 1

$a\sqrt 3 = \sqrt (a^{2} \times 3)$ because we proved that left hand side equals right hand side when we substituted an integer for a.
$a\sqrt 3 = \sqrt (a^{2} \times 3)$ a = 2 We substitute 2 for a $2 \sqrt 3 = \sqrt (2^{2} \times 3)$ $2 \sqrt 3 = \sqrt (12)$ Two factors of 12 are 4 and 3 $2 \sqrt 3 = \sqrt (4 \times 3)$ The square root of 4 is 2 because 2 x 2 = 4 $2 \sqrt 3 = 2 \sqrt 3$