Add 510−−√ + 10−−√ .(1 point) Responses 60−−√ Start Root 60 End Root 620−−√ 6 Start Root 20 End Root 25−−√ Start Root 25 End Root 610−−√
Using the laws of square roots, we can simplify the expression as follows:
√510 + √10
The prime factorization of 510 is 2 * 3 * 5 * 17. To simplify the square root, we group the numbers that appear in pairs inside the square root:
√(2^2 * 3 * 5 * 17) = 2√(3 * 5 * 17)
The prime factorization of 10 is 2 * 5, which can be written as √(2^2 * 5) = 2√5
Now we can substitute these simplified values back into the original expression:
2√(3 * 5 * 17) + 2√5
Since both terms have a common factor of 2, we can factor it out:
2(√(3 * 5 * 17) + √5)
Now, we cannot simplify this expression any further. Therefore, the final answer is 2(√(3 * 5 * 17) + √5).