Question

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which of the following is equivalent to the expression below \sqrt{36x^3}

Answer 1

`\\ \rm\Rrightarrow √(36x^3)`

`\\ \rm\Rrightarrow √(6^2x^3)`

`\\ \rm\Rrightarrow 6x^{3* (1)/(2)}`

`\\ \rm\Rrightarrow 6x^{(3)/(2)}`

Answer 2

`\textsf{D)}\quad6x^{(3)/(2)}`

Explanation:

`\textsf{Apply radical rule} \quad√(ab)=√(a)√(b):`

`\begin{aligned}\implies √(36x^3) &=√(36)√(x^3)\\ & =6√(x^3)\end{aligned}`

`\textsf{Apply radical rule} \quad\sqrt[n]{a}=a^{(1)/(n)}:`

`\implies 6√(x^3)=6(x^3)^{(1)/(2)}`

`\textsf{Apply radical rule} \quad(a^b)^c=a^(bc):`

`\implies 6(x^3)^{(1)/(2)}=6x^{(3)/(2)}`