Which is the exact value of the expression sqrt 32- sqrt 50 + sqrt 128
2 sqrt 7
7 sqrt 2
22 sqrt 2
2 sqrt 55
sqrt(32)=sqrt(2)*sqrt(16)=sqrt(2)*4
sqrt(50)=sqrt(2)*sqrt(25)=sqrt(2)*5
sqrt(128)=sqrt(2)*sqrt(64)=sqrt(2)*8
sqrt(32)-sqrt(50)+sqrt(128)=
sqrt(2)*4-sqrt(2)*5+sqrt(2)*8=
sqrt(2)*(4-5+8)=
sqrt(2)*7
OR
7*sqrt(2)
To simplify the expression sqrt 32 - sqrt 50 + sqrt 128, we need to simplify each individual term under the square root and then combine the terms.
1. Simplifying sqrt 32:
We can write 32 as a product of perfect squares. The largest perfect square that divides 32 is 16, so we can rewrite 32 as 16 * 2. Therefore, sqrt 32 can be simplified as sqrt(16 * 2), which is equal to sqrt(16) * sqrt(2) = 4 * sqrt(2) = 4sqrt(2).
2. Simplifying sqrt 50:
Similar to above, we can write 50 as a product of perfect squares. The largest perfect square that divides 50 is 25, so we can rewrite 50 as 25 * 2. Therefore, sqrt 50 can be simplified as sqrt(25 * 2), which is equal to sqrt(25) * sqrt(2) = 5 * sqrt(2) = 5sqrt(2).
3. Simplifying sqrt 128:
Again, we can write 128 as a product of perfect squares. The largest perfect square that divides 128 is 64, so we can rewrite 128 as 64 * 2. Therefore, sqrt 128 can be simplified as sqrt(64 * 2), which is equal to sqrt(64) * sqrt(2) = 8 * sqrt(2) = 8sqrt(2).
Now let's substitute the simplified values back into the expression:
Original expression: sqrt 32 - sqrt 50 + sqrt 128
Substituting the simplified values: 4sqrt(2) - 5sqrt(2) + 8sqrt(2)
Combining like terms: (4 - 5 + 8) * sqrt(2) = 7 * sqrt(2)
Hence, the exact value of the expression sqrt 32 - sqrt 50 + sqrt 128 is 7sqrt(2).
Therefore, the correct option is 7 sqrt 2.