Add 321√ + 721√.(1 point)
To add the terms 321√ and 721√, you simply combine the coefficients and keep the radical (√) the same.
So, the sum of 321√ + 721√ is:
(321 + 721)√ = 1042√
To add the terms 321√ and 721√, we need to simplify the square roots first, and then add the terms together.
Let's start with 321√. We need to find the square root of 321.
Since 321 is not a perfect square, we can simplify it by finding the factors of 321. The prime factorization of 321 is 3 * 107.
Now, we can rewrite 321√ as √(3 * 107).
Using the property of square roots that √(ab) = √a * √b, we can simplify further:
√(3 * 107) = √3 * √107
Now, let's move on to 721√. We need to find the square root of 721.
Since 721 is not a perfect square, we can simplify it by finding the factors of 721. The prime factorization of 721 is 7 * 103.
Now, we can rewrite 721√ as √(7 * 103).
Using the property of square roots that √(ab) = √a * √b, we can simplify further:
√(7 * 103) = √7 * √103
Now that we have simplified both terms, we can add them together:
√3 * √107 + √7 * √103
Since the square roots have different radicands (numbers inside the square root), we cannot combine them further. Therefore, the sum of 321√ and 721√ is:
√3 * √107 + √7 * √103
To add these two square roots, we need to simplify each term individually and then combine them. Let's break it down step by step:
Step 1: Simplify the first square root (321√):
To simplify this square root, we need to find the largest perfect square that is a factor of 321. In this case, the largest perfect square that divides 321 is 9 (since 9 * 36 = 324). Therefore, we can simplify 321√ as 9√(36), which equals 9 * 6 = 54.
So, 321√ simplifies to 54.
Step 2: Simplify the second square root (721√):
We follow the same process to simplify this square root. The largest perfect square that divides 721 is 25 (since 25 * 29 = 725). Hence, we can simplify 721√ as 25√(29).
Step 3: Combine the simplified expressions:
Since the two square roots have different radicals (√36 and √29), we cannot combine them directly. Therefore, the sum of 321√ + 721√ remains as 54 + 25√(29).
So, the final answer is 54 + 25√(29).