Question

Rewrite the radical by extracting all possible roots and write your answer in radical form 75x4y7−−−−−−√

Answer 1

Answer:

$\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}$

Step-by-step explanation:

Given

$\sqrt{75x^4y^7$

Required

Rewrite

Express 75 as 25 * 3

$\sqrt{75x^4y^7} = \sqrt{25 * 3x^4y^7}$

Split

$\sqrt{75x^4y^7} = \sqrt{25} * \sqrt{3x^4y^7}$

This gives:

$\sqrt{75x^4y^7} = 5 * \sqrt{3x^4y^7}$

Express y^7 as y^6 * y

$\sqrt{75x^4y^7} = 5 * \sqrt{3*x^4 * y^6 * y}$

Split

$\sqrt{75x^4y^7} = 5 * \sqrt{3} *\sqrt{x^4} * \sqrt{y^6} * \sqrt{y}$

Express square roots as exponents

$\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^{(4 * \frac{1}{2})} * y^{(6* \frac{1}{2})} * \sqrt{y}$

$\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^2 * y^3 * \sqrt{y}$

Rewrite the factors

$\sqrt{75x^4y^7} = 5 * x^2 * y^3* \sqrt{3} * \sqrt{y}$

$\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3} * \sqrt{y}$

Combine roots

$\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3y}$

$\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}$