Bet...but you really need to learn how to to this bc you use this in all types of math
All you have to do is distribute then combine like terms
Zoom in
Step-by-step explanation:
roots as exponents are fractions
if there is no root number next to the radical sign its assumed that its 1/2
3√2 is 2^(1/3)
√3 is 3^(1/2)
4√3 is 3^(1/4)
5√2 is 2^(1/5)
We can apply the following properties of radicals:
![\begin{gathered} \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\Rightarrow\text{ Product property} \\ \sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\Rightarrow\text{ Quotient property} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Ccdot%5Csqrt%5Bn%5D%7Bb%7D%5CRightarrow%5Ctext%7B%20Product%20property%7D%20%5C%5C%20%5Csqrt%5Bn%5D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Csqrt%5Bn%5D%7Ba%7D%7D%7B%5Csqrt%5Bn%5D%7Bb%7D%7D%5CRightarrow%5Ctext%7B%20Quotient%20property%7D%20%5Cend%7Bgathered%7D)
Then, we have:
![\begin{gathered} \text{ Apply the product property} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{7}{8}\cdot\frac{7}{18}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{7\cdot7}{8\cdot18}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{49}{144}} \\ \text{ Apply the quotient property} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\frac{\sqrt[]{49}}{\sqrt[]{144}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\frac{7}{12} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7B%20Apply%20the%20product%20property%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%5Ccdot%5Cfrac%7B7%7D%7B18%7D%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B7%5Ccdot7%7D%7B8%5Ccdot18%7D%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B49%7D%7B144%7D%7D%20%5C%5C%20%5Ctext%7B%20Apply%20the%20quotient%20property%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Cfrac%7B%5Csqrt%5B%5D%7B49%7D%7D%7B%5Csqrt%5B%5D%7B144%7D%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B8%7D%7D%5Ccdot%5Csqrt%5B%5D%7B%5Cfrac%7B7%7D%7B18%7D%7D%3D%5Cfrac%7B7%7D%7B12%7D%20%5Cend%7Bgathered%7D)
Therefore, the choice that is equivalent to the given product is: