Solve for: sqrt(45x^9y^{49)z^{36}}

Expression: $\sqrt{ 45{x}^{9}{y}^{49}{z}^{36} }$

Write the expression as a product where the root of one of the factors can be evaluated

$\sqrt{ 9 \times 5{x}^{9}{y}^{49}{z}^{36} }$

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 $2$

$3{x}^{4}{y}^{24}{z}^{18}\sqrt{ 5xy }$