$\sqrt{ 9 \times 5{x}^{9}{y}^{49}{z}^{36} }$
Rewrite the exponent as a sum where one of the addends is a multiple of the index$\sqrt{ 9 \times 5{x}^{8+1}{y}^{49}{z}^{36} }$
Rewrite the exponent as a sum where one of the addends is a multiple of the index$\sqrt{ 9 \times 5{x}^{8+1}{y}^{48+1}{z}^{36} }$
Write the expression in exponential form with the base of $3$$\sqrt{ {3}^{2} \times 5{x}^{8+1}{y}^{48+1}{z}^{36} }$
Use ${a}^{m+n}={a}^{m} \times {a}^{n}$ to expand the expression$\sqrt{ {3}^{2} \times 5{x}^{8} \times {x}^{1}{y}^{48+1}{z}^{36} }$
Use ${a}^{m+n}={a}^{m} \times {a}^{n}$ to expand the expression$\sqrt{ {3}^{2} \times 5{x}^{8} \times {x}^{1}{y}^{48} \times {y}^{1}{z}^{36} }$
Any expression raised to the power of $1$ equals itself$\sqrt{ {3}^{2} \times 5{x}^{8} \times x{y}^{48} \times {y}^{1}{z}^{36} }$
Any expression raised to the power of $1$ equals itself$\sqrt{ {3}^{2} \times 5{x}^{8} \times x{y}^{48} \times y{z}^{36} }$
The root of a product is equal to the product of the roots of each factor$\sqrt{ {3}^{2} }\sqrt{ {x}^{8} }\sqrt{ {y}^{48} }\sqrt{ {z}^{36} }\sqrt{ 5xy }$
Reduce the index of the radical and exponent with $2$$3\sqrt{ {x}^{8} }\sqrt{ {y}^{48} }\sqrt{ {z}^{36} }\sqrt{ 5xy }$
Reduce the index of the radical and exponent with $2$$3{x}^{4}\sqrt{ {y}^{48} }\sqrt{ {z}^{36} }\sqrt{ 5xy }$
Reduce the index of the radical and exponent with $2$$3{x}^{4}{y}^{24}\sqrt{ {z}^{36} }\sqrt{ 5xy }$
Reduce the index of the radical and exponent with $2$$3{x}^{4}{y}^{24}{z}^{18}\sqrt{ 5xy }$