Add 321−−√ + 721−−√.(1 point) Responses 24 −−−√ + 28−−√ Start Root 24 End Root plus Start Root 28 End Root 1042−−√ 10 Start Root 42 End Root 52−−√ Start Root 52 End Root 1021−−√
The simplified expression would be 10−−√ + 21−−√.
To calculate the expression 321−−√ + 721−−√, we need to first simplify each square root term separately, and then add the results together.
Let's start with the first term, 321−−√. To simplify this square root, we need to find the largest perfect square that is a factor of 32. In this case, it is 16 because 16 * 2 = 32. Therefore, we can rewrite 321−−√ as 16√2.
Now let's simplify the second term, 721−−√. Similarly, we need to find the largest perfect square that is a factor of 72. In this case, it is 36 because 36 * 2 = 72. Therefore, we can rewrite 721−−√ as 36√2.
Now we can add these two simplified square roots together:
16√2 + 36√2 = (16 + 36)√2 = 52√2.
So, the final result of the expression 321−−√ + 721−−√ is 52−−√.
To simplify the expression 321−−√ + 721−−√, follow these steps:
Step 1: Simplify the square roots individually.
Start Root 24 End Root = √24
Start Root 28 End Root = √28
Step 2: Simplify the square roots further.
√24 = √(4 * 6) = 2√6
√28 = √(4 * 7) = 2√7
Step 3: Add the simplified square roots.
2√6 + 2√7 = 2(√6 + √7)
The simplified expression is 2(√6 + √7).