Add 510−−√ + 10−−√
To add these two expressions, we need to simplify each expression first.
Let's simplify 510 −− √:
√10 can be simplified as 10^(1/2). Therefore, 510 −− √ = 510 − 10^(1/2).
Now simplifying 10 −− √:
√10 can be simplified as 10^(1/2). Therefore, 10 −− √ = 10 − 10^(1/2).
Now let's add the simplified expressions:
(510 − 10^(1/2)) + (10 − 10^(1/2))
The common term between the two expressions is -10^(1/2).
Therefore, (510 − 10^(1/2)) + (10 − 10^(1/2)) = 510 + 10 = 520.
To add 510−−√ and 10−−√, we need to simplify the square roots first.
The square root of 510 can be written as √(510) and the square root of 10 can be written as √(10).
So, the expression becomes √(510) + √(10).
Unfortunately, these square roots cannot be simplified further since there are no perfect square factors.
Therefore, the final answer is √(510) + √(10).
To add the numbers 510−√ and 10−√, we can follow these steps:
Step 1: Simplify the square roots
- Start by simplifying the square root of 510 and the square root of 10.
- The square root of 510 can be simplified as follows:
- Find the prime factorization of 510: 510 = 2 x 3 x 5 x 17
- Since there is no pair of identical factors, you cannot simplify the square root of 510 any further.
- The square root of 10 can be simplified as follows:
- Find the prime factorization of 10: 10 = 2 x 5
- Since there is no pair of identical factors, you cannot simplify the square root of 10 any further.
- So, we have 510−−√ + 10−−√
Step 2: Add the numbers
- Now, add the two numbers:
510−−√ + 10−−√ = √510 + √10
Step 3: Combine the square roots
- Since the numbers inside the square roots are not the same, we cannot combine them into a single square root.
- So, the final answer to the addition is √510 + √10.
Note: It is not possible to simplify the addition of these specific square roots any further because the numbers inside the square roots do not have any common factors.