Calculate: sqrt(6x^5)

Expression: $\sqrt{ 6{x}^{5} }$

Rewrite the exponent as a sum where one of the addends is a multiple of the index

$\sqrt{ 6{x}^{4+1} }$

Use ${a}^{m+n}={a}^{m} \times {a}^{n}$ to expand the expression

$\sqrt{ 6{x}^{4} \times {x}^{1} }$

Any expression raised to the power of $1$ equals itself

$\sqrt{ 6{x}^{4} \times x }$

The root of a product is equal to the product of the roots of each factor

$\sqrt{ {x}^{4} }\sqrt{ 6x }$

Reduce the index of the radical and exponent with $2$

${x}^{2}\sqrt{ 6x }$