Add 3sqrt(21) + 7sqrt(21) (1 point)
10sqrt(21)
sqrt(24) + sqrt(28)
10sqrt(42)
sqrt(52)
2√(21)+7√(21)= 9√(21) (1 point)
To add 3sqrt(21) + 7sqrt(21):
Step 1: Combine the coefficients: 3 + 7 = 10.
Step 2: Keep the same radical term: sqrt(21).
Therefore, the sum is 10sqrt(21).
To simplify sqrt(24) + sqrt(28):
Step 1: Simplify the radical terms: sqrt(24) = 2sqrt(6) and sqrt(28) = 2sqrt(7).
Step 2: Combine the simplified radical terms: 2sqrt(6) + 2sqrt(7).
Therefore, the sum can be written as 2sqrt(6) + 2sqrt(7).
To simplify sqrt(52):
Step 1: Simplify the radical term: sqrt(52) = sqrt(4*13) = 2sqrt(13).
Therefore, sqrt(52) can be simplified as 2sqrt(13).
To solve the given expression, you can use the following steps:
Step 1: Combine like terms
You need to add the terms with the same radical coefficient.
3√21 + 7√21 = (3 + 7)√21 = 10√21
Therefore, 3√21 + 7√21 = 10√21.
Step 2: Simplify the expression further.
If there are other terms involving different square roots, you can simplify them by finding the largest perfect square factor that can be extracted.
√24 + √28
For √24, the largest perfect square that can be extracted is 4, as 24 = 4 × 6, so √24 = 2√6.
For √28, the largest perfect square that can be extracted is 4, as 28 = 4 × 7, so √28 = 2√7.
Therefore, √24 + √28 = 2√6 + 2√7.
Step 3: Combine like terms (if applicable)
Since there are no like terms in √6 and √7 (i.e., they cannot be combined), the simplified expression is already in its simplest form:
√24 + √28 = 2√6 + 2√7.
Finally, if you have any other expressions, such as √52, you can follow the same process to simplify it further by extracting the largest perfect square.
I hope this helps! Let me know if you have any further questions.