The quantity sqrt(45)- 2sqrt(5) +sqrt(360/2) can be expressed as sqrt(N), where N is an integer. Find N.
* the whole fraction 360/2 is squarerooted.
To find the value of sqrt(45) - 2sqrt(5) + sqrt(360/2) and express it as sqrt(N), where N is an integer, we need to simplify the expression.
First, let's simplify each term within the expression:
- sqrt(45) can be simplified as sqrt(9 * 5). Since sqrt(9) = 3, we have sqrt(45) = 3sqrt(5).
- sqrt(360/2) can be simplified as sqrt(180), which can further be simplified as sqrt(36 * 5). Since sqrt(36) = 6, we have sqrt(360/2) = 6sqrt(5).
Now, let's substitute these simplified values back into the expression:
sqrt(45) - 2sqrt(5) + sqrt(360/2)
= 3sqrt(5) - 2sqrt(5) + 6sqrt(5)
Combining like terms, we have:
= (3 - 2 + 6) sqrt(5)
= 7sqrt(5)
Therefore, the value of sqrt(45) - 2sqrt(5) + sqrt(360/2) can be expressed as sqrt(N), where N = (7^2) * (5) = 49 * 5 = 245.
So, N = 245.
To find the value of sqrt(45) - 2sqrt(5) + sqrt(360/2), we can simplify each term individually, combine like terms, and then express the resulting expression as sqrt(N), where N is an integer.
1. Simplify sqrt(45):
sqrt(45) = sqrt(9 * 5) = sqrt(9) * sqrt(5) = 3 * sqrt(5)
2. Simplify sqrt(360/2):
sqrt(360/2) = sqrt(180) = sqrt(36 * 5) = sqrt(36) * sqrt(5) = 6 * sqrt(5)
Now, let's combine the simplified terms:
3 * sqrt(5) - 2sqrt(5) + 6 * sqrt(5)
Combining like terms, we have:
(3 - 2 + 6) * sqrt(5) = 7 * sqrt(5)
Therefore, the quantity sqrt(45) - 2sqrt(5) + sqrt(360/2) can be expressed as sqrt(N), where N = (7^2) * (5) = 245.