Question

which choices are equivalent to the expression below. check all apply sqrt 2 x sqrt 5 x sqrt 10A. 10B. 15C. 10 over sqrt 10D. 100C. 2 over sqrt 25F. SQRT 100

Answer 1

`\begin{gathered} \sqrt[]{2}\cdot\sqrt[]{5}\cdot\sqrt[]{10} \\ \sqrt[]{2}\cdot\sqrt[]{5}\cdot\sqrt[]{2\cdot5} \\ \sqrt[]{2^2}\cdot\sqrt[]{5^2} \\ 2\cdot5=10 \end{gathered}`

The first is to decouple the 10 into 2 * 5 and extract the values within the root. The other is to enter all the values to the same root and calculate in general

`\begin{gathered} \sqrt[]{2}\cdot\sqrt[]{5}\cdot\sqrt[]{10}=\sqrt[]{2\cdot5\cdot10} \\ \sqrt[]{100}=10 \end{gathered}`