Question

(4, \sqrt{200x^{11}y^{10}z^{27}}

Explanation:

Step1: Split radical into factors

$\sqrt{200x^{11}y^{10}z^7} = \sqrt{100 \times 2 \times x^{10} \times x \times y^{10} \times z^6 \times z}$

Step2: Simplify perfect squares

$\sqrt{100} \times \sqrt{x^{10}} \times \sqrt{y^{10}} \times \sqrt{z^6} \times \sqrt{2xz}$

Step3: Compute square roots of perfect squares

$10 \times x^5 \times y^5 \times z^3 \times \sqrt{2xz}$

Step4: Combine terms outside radical

$10x^5y^5z^3\sqrt{2xz}$

Answer:

$10x^5y^5z^3\sqrt{2xz}$