Add 321−−√ + 721−−√ .(1 point)
Responses
1021−−√
10 Start Root 21 End Root
24 −−−√ + 28−−√
Start Root 24 End Root plus Start Root 28 End Root
52−−√
Start Root 52 End Root
1042−−√
Start Root 1042 End Root
To add √321 + √721, we need to simplify each square root separately.
Step 1: Simplify √321
The square root of 321 can be written as √(10^2 * 32 + 1) = 10√32+√1 = 10√32 + 1√1
Step 2: Simplify √721
The square root of 721 can be written as √(10^2 * 72 + 1) = 10√72+√1 = 10√72 + 1√1
Step 3: Add the simplified square roots
Now, we can add the simplified square roots together:
10√32 + 1√1 + 10√72 + 1√1 = (10√32 + 10√72) + (1√1 + 1√1)
Step 4: Combine like terms
The terms 10√32 and 10√72 cannot be simplified further as they have different radicands (numbers inside the square root). Similarly, the terms 1√1 + 1√1 cannot be simplified further.
Therefore, the sum of √321 + √721 is:
10√32 + 10√72 + 1√1 + 1√1 = 10√32 + 10√72 + 2√1
So, the final answer is 10√32 + 10√72 + 2√1.
To solve the expression 321−−√ + 721−−√, we need to calculate the square roots of 321 and 721 separately and then add them together.
First, let's find the square root of 321. We can use a scientific calculator or an online calculator. Simply input the number 321 and find the square root.
√321 ≈ 17.93
Next, let's find the square root of 721.
√721 ≈ 26.87
Finally, we add the two square roots together:
17.93 + 26.87 ≈ 44.8
Therefore, the solution to the expression 321−−√ + 721−−√ is approximately 44.8.
If you'd like to do this calculation again in the future, you can use any scientific calculator or an online calculator by entering the expressions separately and then adding the results together.