Answer:
The correct option is 3.
Step-by-step explanation:
The given expression is
[tex]\sqrt{8x^7y^8}[/tex]
Where x≥0.
The given expression can be written as
[tex]\sqrt{2^3x^7y^8}[/tex]
[tex]\sqrt{2^2\cdot 2\cdot x^6\cdot x\cdot y^8}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
Now combine the terms having even powers.
[tex]\sqrt{(2^2\cdot x^6\cdot y^8)\cdot (2\cdot x)}[/tex]
[tex]\sqrt{(2x^3y^4)^2\cdot (2x)}[/tex] [tex][\because (mn)^x=m^xn^x][/tex]
[tex]2x^3y^4\sqrt{2x}[/tex] [tex][\because \sqrt{x^2}=x][/tex]
The given expression is equivalent to [tex]2x^3y^4\sqrt{2x}[/tex]. Thus option 3 is correct.
