Answer :
Answer:
Step-by-step explanation:
The answer is 6√200, or option B on edg.
Answer:
[tex]\sqrt[6]{200}[/tex]
Step-by-step explanation:
We have been an radical expression [tex]\sqrt[3]{5}\times \sqrt{2}[/tex] and we are asked to find the product of our given expression.
We can write our given numbers as:
[tex]\sqrt[3]{5}=\sqrt[3*2]{5^2}=\sqrt[6]{5^2}[/tex]
[tex]\sqrt{2}=\sqrt[2]{2}=\sqrt[3*2]{2^3}=\sqrt[6]{2^3}[/tex]
Using exponent property [tex]\sqrt[m]{a}=a^{\frac{1}{m}}[/tex] we can write our expression as:
[tex](5^2)^{\frac{1}{6}}\times (2^3)^{\frac{1}{6}}[/tex]
Using exponent property [tex](a^m)^n=a^{m*n}[/tex] we can write our expression as:
[tex](5^2\times 2^3)^{\frac{1}{6}}[/tex]
[tex](25\times 8)^{\frac{1}{6}}[/tex]
[tex](200)^{\frac{1}{6}}[/tex]
Upon writing our answer as radical we will get: [tex]\sqrt[6]{200}[/tex]
Therefore, the product of our expression will be: [tex]\sqrt[6]{200}[/tex].