Question

The following are equivalent radicals

3√3 = √27
-
3√6 = √54
3√7 = √63
What would be an equivalent form of 3√11 ? Explain
how you know.

Answer 1

To find an equivalent form of 3√11, we need to simplify the radical expression. We can start by factoring 11 into its prime factors:

11 = 1 x 11

Since there are no perfect squares that divide evenly into 11, we cannot simplify the radical any further. Therefore, an equivalent form of 3√11 is simply 3√11.

We can confirm this by rationalizing the denominator of the radical expression:

3√11 * (√11/√11) = 3√(11*11)/√121 = 3√121/√121 = 3(11)/11 = 3

This shows that 3√11 is in simplest form and cannot be simplified any further