Answer:
[tex]\sqrt{8x^7y^8[/tex][tex]= 2x^3y^4 * \sqrt{2x}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{8x^7y^8[/tex]
Required
Evaluate
[tex]\sqrt{8x^7y^8[/tex]
Separate each factor with multiplication sign
[tex]\sqrt{8*x^7*y^8[/tex]
Express 8 as 4 * 2 and [tex]x^7[/tex] as [tex]x^6 * x[/tex]
[tex]\sqrt{4 * 2 *x^6 * x*y^8[/tex]
Split each factor
[tex]\sqrt{4} * \sqrt{2} *\sqrt{x^6} * \sqrt{x}*\sqrt{y^8}[/tex]
Evaluate [tex]\sqrt4[/tex]
[tex]2 * \sqrt{2} *\sqrt{x^6} * \sqrt{x}*\sqrt{y^8}[/tex]
Apply law of indices:
[tex]2 * \sqrt{2} * x^{6*\frac{1}{2}} * \sqrt{x} * y^{8*\frac{1}{2}}[/tex]
[tex]2 * \sqrt{2} * x^3 * \sqrt{x} * y^4[/tex]
Reorder
[tex]2* x^3 * y^4 * \sqrt{2} * \sqrt{x}[/tex]
[tex]2x^3y^4 * \sqrt{2} * \sqrt{x}[/tex]
[tex]2x^3y^4 * \sqrt{2*x}[/tex]
[tex]2x^3y^4 * \sqrt{2x}[/tex]
[tex]2x^3y^4 \sqrt {2x[/tex]
Hence:
[tex]\sqrt{8x^7y^8[/tex][tex]= 2x^3y^4 * \sqrt{2x}[/tex]
Answer: It is C or 2x^3y^4 square root2x.
Step-by-step explanation: Checked on my calculator it is correct.
