Answer:
[tex]\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{75x^4y^7[/tex]
Required
Rewrite
Express 75 as 25 * 3
[tex]\sqrt{75x^4y^7} = \sqrt{25 * 3x^4y^7}[/tex]
Split
[tex]\sqrt{75x^4y^7} = \sqrt{25} * \sqrt{3x^4y^7}[/tex]
This gives:
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3x^4y^7}[/tex]
Express y^7 as y^6 * y
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3*x^4 * y^6 * y}[/tex]
Split
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} *\sqrt{x^4} * \sqrt{y^6} * \sqrt{y}[/tex]
Express square roots as exponents
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^{(4 * \frac{1}{2})} * y^{(6* \frac{1}{2})} * \sqrt{y}[/tex]
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^2 * y^3 * \sqrt{y}[/tex]
Rewrite the factors
[tex]\sqrt{75x^4y^7} = 5 * x^2 * y^3* \sqrt{3} * \sqrt{y}[/tex]
[tex]\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3} * \sqrt{y}[/tex]
Combine roots
[tex]\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3y}[/tex]
[tex]\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}[/tex]
