which expression is equivalent to $sqrt{400h^{8}j^{4}k^{6}}$?\n$20h^{4}j^{2}|k^{3}|$\n$20h^{6}j^{2}k^{4}$\n$2…

which expression is equivalent to $sqrt{400h^{8}j^{4}k^{6}}$?\n$20h^{4}j^{2}|k^{3}|$\n$20h^{6}j^{2}k^{4}$\n$200h^{4}j^{2}|k^{3}|$\n$200h^{6}j^{2}k^{4}$

which expression is equivalent to $sqrt{400h^{8}j^{4}k^{6}}$?\n$20h^{4}j^{2}|k^{3}|$\n$20h^{6}j^{2}k^{4}$\n$200h^{4}j^{2}|k^{3}|$\n$200h^{6}j^{2}k^{4}$

Answer

Explanation:

Step1: Break - down the square - root of the coefficient

$\sqrt{400}=20$

Step2: Apply the square - root rule for variables with exponents

For $h^{8}$, $\sqrt{h^{8}} = h^{\frac{8}{2}}=h^{4}$; for $j^{4}$, $\sqrt{j^{4}} = j^{\frac{4}{2}}=j^{2}$; for $k^{6}$, $\sqrt{k^{6}}=\vert k^{3}\vert$ (since we need to account for the non - negative result of the square root when dealing with real numbers and an even root of an even - powered variable).

Step3: Combine the results

The expression $\sqrt{400h^{8}j^{4}k^{6}}$ is equivalent to $20h^{4}j^{2}\vert k^{3}\vert$

Answer:

$20h^{4}j^{2}\vert k^{3}\vert$