Add 321−−√ + 721−−√ .(1 point) Responses
10 21−−√ 10 Start Root 21 End Root
10 42−−√ 10 Start Root 42 End Root 24 −−−√ + 28−−√ Start Root 24 End Root plus Start Root 28 End Root
52−−√ Start Root 52 End Root
52−−√ Start Root 52 End Root
To solve the equation 321−−√ + 721−−√, we can simplify each square root separately.
Step 1: Simplify √21
Start with the square root of 21, which cannot be simplified any further. So, the square root of 21 remains as it is.
Step 2: Simplify √42
Start with the square root of 42. By factoring 42 as 2 * 21, we can simplify it.
√42 = √(2 * 21)
= √2 * √21
Now we know that √21 cannot be simplified further, so the square root of 42 remains as √2 * √21.
Step 3: Simplify the expression
Now that we have simplified both square roots, we can add them together.
√21 + √42 = √21 + √2 * √21
Since both terms have a common factor of √21, we can factor it out.
√21(1 + √2)
So, the simplified expression is √21(1 + √2).
To add √321 + √721, follow these steps:
Step 1: Simplify each square root individually.
√321 = 10√21
√721 = 10√42
Step 2: Add the simplified square roots.
10√21 + 10√42 = 10(√21 + √42)
Step 3: Combine the square roots as much as possible.
√21 and √42 cannot be simplified further since they are not perfect squares. Therefore, the answer is:
10(√21 + √42)