Question

Combine these radicals. 8 square root 5 + 2 square root 45

Answer 1

14√5

Explanation:

8√5 + 2√45

= 8√5 + 6√5

= 14√5

Hope this helps

Answer 2

`\boxed {\boxed {\sf 14 √(5)}}`

Explanation:

We are asked to combine the radicals. We have the following expression:

`8 √(5) + 2 √(45)`

Currently, we cannot combine these radicals. The value under the square root is not the same for both terms.

However, we can simplify the radical 2 √45 because the value under the radical is divisible by a perfect square.

45 can be divided by 9 (the perfect square) for a quotient of 5. So, we can simplify the radical using this information.

Break the radical into 2 radicals: 9 and 5.

`8 √(5)+ 2 √(9)√(5)`

Notice that a perfect square is under the radical. √9 can be simplifed to 3.

`8 √(5)+ 2 *3 √(5)`

Multiply 2 and 3.

`8 √(3) + 6 √(5)`

Now the value under the radical is the same for both terms, and we can add the numbers in front of the radicals.

`14 √(5)`

The radicals combined is equal to 14√5