$\sqrt{ 25 \times 6{x}^{16}{y}^{9} }$
Rewrite the exponent as a sum where one of the addends is a multiple of the index$\sqrt{ 25 \times 6{x}^{16}{y}^{8+1} }$
Write the expression in exponential form with the base of $5$$\sqrt{ {5}^{2} \times 6{x}^{16}{y}^{8+1} }$
Use ${a}^{m+n}={a}^{m} \times {a}^{n}$ to expand the expression$\sqrt{ {5}^{2} \times 6{x}^{16}{y}^{8} \times {y}^{1} }$
Any expression raised to the power of $1$ equals itself$\sqrt{ {5}^{2} \times 6{x}^{16}{y}^{8} \times y }$
The root of a product is equal to the product of the roots of each factor$\sqrt{ {5}^{2} }\sqrt{ {x}^{16} }\sqrt{ {y}^{8} }\sqrt{ 6y }$
Reduce the index of the radical and exponent with $2$$5\sqrt{ {x}^{16} }\sqrt{ {y}^{8} }\sqrt{ 6y }$
Reduce the index of the radical and exponent with $2$$5{x}^{8}\sqrt{ {y}^{8} }\sqrt{ 6y }$
Reduce the index of the radical and exponent with $2$$5{x}^{8}{y}^{4}\sqrt{ 6y }$