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

2 Answers

3 votes

Answer

14√5

Explanation:

8√5 + 2√45

= 8√5 + 6√5

= 14√5

Hope this helps

User Dris
by
6.4k points
4 votes

Answer:


\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

User Korashen
by
7.9k points