add 3 square root 21 + 7 square root 21
10 square root 21
10 square root 42
square root 52
square root 24 + square root 28
10√21 + √52
To simplify the expression "3√21 + 7√21", combine the terms with the same radical.
Step 1: Combine the terms with √21.
3√21 + 7√21 = (3 + 7)√21 = 10√21
So, the simplified expression is 10√21.
Next, let's simplify the expression "√52".
To simplify a radical, we need to find the largest perfect square that divides 52.
Step 2: Simplify √52.
We can rewrite 52 as 4 * 13. Since 4 is a perfect square, we can simplify √52 as √(4 * 13) = 2√13.
So, √52 simplifies to 2√13.
Now, let's simplify the expression "√24 + √28".
Step 3: Simplify √24.
We can rewrite 24 as 4 * 6. Since 4 is a perfect square, we can simplify √24 as √(4 * 6) = 2√6.
Step 4: Simplify √28.
We can rewrite 28 as 4 * 7. Since 4 is a perfect square, we can simplify √28 as √(4 * 7) = 2√7.
So, the expression "√24 + √28" simplifies to 2√6 + 2√7.
To simplify the expression "3 square root 21 + 7 square root 21", we can combine the terms that have the same square root.
We have "3 square root 21" and "7 square root 21". Since both terms have the same square root of 21, we can add their coefficients (3 and 7) together and keep the square root term the same:
(3 square root 21) + (7 square root 21) = (3 + 7) square root 21
Therefore, the simplified expression is "10 square root 21".
As for the expression "10 square root 21", it is not simplified further unless we have additional information about the value of √21.
For the expression "10 square root 42", it cannot be further simplified unless we have additional information about the value of √42.
For the expression "√52", we can simplify it by identifying any perfect square factors within 52. In this case, 4 is a perfect square factor of 52 (4 x 13 = 52). We can rewrite it as:
√(4 x 13) = √4 x √13 = 2√13
Therefore, the simplified expression is "2 square root 13".
Lastly, for the expression "√24 + √28", we can simplify it by identifying any perfect square factors within 24 and 28. In this case, both 4 and 7 are perfect square factors of 24 and 28 respectively. We can rewrite it as:
√(4 x 6) + √(4 x 7) = √4 x √6 + √4 x √7 = 2√6 + 2√7
Therefore, the simplified expression is "2 square root 6 + 2 square root 7".