Add 321+ 7√21.
10√42
10√21
√24 + √28
√52
To add 321 + 7√21, we keep the whole number part and add the coefficient of the square root terms separately. So, the answer is 321 + 7√21.
To simplify 10√42, we can find the largest perfect square that is a factor of 42, which is 6. So, we can write this as 10√6 * √7. Therefore, the simplified form is 10√6√7 or 10√42.
To simplify 10√21, there are no perfect square factors of 21. Therefore, this expression cannot be simplified any further. So, the simplified form of 10√21 remains as 10√21.
To simplify √24 + √28, we can find the largest perfect square factor of each number. The largest perfect square factor of 24 is 4, and the largest perfect square factor of 28 is 4 as well. So, this expression can be written as 2√6 + 2√7. Therefore, the simplified form is 2√6 + 2√7.
To simplify √52, we can find the largest perfect square factor of 52, which is 4. So, this expression can be written as 2√13. Therefore, the simplified form is 2√13.
To solve these expressions, we will simplify each one step by step:
1. 321 + 7√21:
No further simplification can be done, so the answer is 321 + 7√21.
2. 10√42:
First, we need to simplify the square root of 42. Since 42 = 6 × 7, we can write 10√42 as 10√(6 × 7). We can then separate it into 10√6 × √7. However, the square root of 6 cannot be further simplified, so the final answer is 10√6√7, or 10√(42).
3. 10√21:
No further simplification can be done, so the answer is 10√21.
4. √24 + √28:
We can simplify each square root separately. The square root of 24 can be written as √(4 × 6), which can then be further simplified to 2√6. The square root of 28 can be written as √(4 × 7), which can be further simplified to 2√7. Therefore, the final answer is 2√6 + 2√7.
5. √52:
We can simplify √52 by writing it as √(4 × 13). Simplifying further, we get 2√13. The final answer is 2√13.
So the simplified expressions are:
1. 321 + 7√21
2. 10√6√7
3. 10√21
4. 2√6 + 2√7
5. 2√13
To add 321 and 7√21, we can combine the terms that are similar. Since 321 is a whole number, it cannot be combined with the square root term 7√21. Therefore, the sum remains as 321 + 7√21.
To simplify 10√42, we first need to find the factors of the number inside the square root. The prime factorization of 42 is 2 × 3 × 7. Since we have a factor of 7 inside the square root, we can simplify it further. The simplified form is 10√(2 × 3 × 7) = 10√14.
Similarly, to simplify 10√21, we need to find the factors of 21. The prime factorization of 21 is 3 × 7. Thus, the simplified form is 10√(3 × 7) = 10√21.
To simplify √24 + √28, first, we can find the factors of 24 and 28. The prime factorization of 24 is 2 × 2 × 2 × 3 = 2^3 × 3. The prime factorization of 28 is 2 × 2 × 7 = 2^2 × 7. Now, we see that we have common factors of 2 inside both square roots. We can simplify as follows:
√24 + √28 = √(2^3 × 3) + √(2^2 × 7)
= 2√3 + 2√7
= 2(√3 + √7)
Finally, to simplify √52, we can find the factors of 52. The prime factorization of 52 is 2 × 2 × 13 = 2^2 × 13. Since we have a factor of 2 inside the square root, we can simplify it further. The simplified form is √(2^2 × 13) = 2√13.
Therefore, the simplified forms of the expressions are:
321 + 7√21
10√14
10√21
2(√3 + √7)
2√13