Answer:
[tex]\sqrt{27x^2y^2}=3xy\:\sqrt{3}[/tex]
Hence, option C is correct.
Step-by-step explanation:
Given the expression
[tex]\sqrt{27x^2y^2}[/tex]
simplifying the expression
[tex]\sqrt{27x^2y^2}=\sqrt{27}\sqrt{x^2}\sqrt{y^2}[/tex]
Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=\sqrt{27}x\sqrt{y^2}[/tex]
Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=\sqrt{27}xy[/tex]
[tex]=xy\sqrt{3^3}[/tex]
[tex]=xy\sqrt{3^2\cdot \:\:3}[/tex]
Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=3xy\:\sqrt{3}[/tex]
Therefore,
[tex]\sqrt{27x^2y^2}=3xy\:\sqrt{3}[/tex]
Hence, option C is correct.
