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schepotkina [342]
3 years ago
10

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

Mathematics
1 answer:
iren2701 [21]3 years ago
6 0

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.

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