Question

Simplify: √27x^2y^2 A) 27xy B) 3xy C) 3xy√3 D) xy√27

Answer 1

Answer:

$\sqrt{27x^2y^2}=3xy\:\sqrt{3}$

Hence, option C is correct.

Step-by-step explanation:

Given the expression

$\sqrt{27x^2y^2}$

simplifying the expression

$\sqrt{27x^2y^2}=\sqrt{27}\sqrt{x^2}\sqrt{y^2}$

Apply radical rule: $\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

               $=\sqrt{27}x\sqrt{y^2}$

Apply radical rule: $\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

                $=\sqrt{27}xy$

                $=xy\sqrt{3^3}$

                 $=xy\sqrt{3^2\cdot \:\:3}$

Apply radical rule: $\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

                  $=3xy\:\sqrt{3}$

Therefore,

$\sqrt{27x^2y^2}=3xy\:\sqrt{3}$

Hence, option C is correct.