How do you evaluate 2root5{ 2} + 2root5{ 64}?

1 Answer
Aug 4, 2017

See a solution process below:

Explanation:

First, we can rewrite the expression as:

2root(5)(2) + 2root(5)(32 * 2) =>

2root(5)(2) + 2root(5)(2^5 * 2)

Now we can use this rule of radicals to simplify the radical on the right side of the expression:

root(n)(color(red)(a) * color(blue)(b)) = root(n)(color(red)(a)) * root(n)(color(blue)(b))

2root(5)(2) + 2root(5)(color(red)(2^5) * color(blue)(2)) =>

2root(5)(2) + 2root(5)(color(red)(2^5))root(5)(color(blue)(2)) =>

2root(5)(2) + (2 * 2root(5)(color(blue)(2))) =>

2root(5)(2) + 4root(5)(color(blue)(2))

We can now factor out the common term of root(5)(3) and combine the remaining terms:

2root(5)(2) + 4root(5)(2) =>

(2 + 4)root(5)(2) =>

6root(5)(2)