sqrt(55) -sqrt(1/55)+sqrt(5/11)=?
To simplify the given expression, we can simplify each square root individually and then combine them.
1. Simplifying √55:
We observe that 55 is not a perfect square, so we can look for its prime factors. The prime factorization of 55 is 5 * 11. Since the square root of 5 and 11 cannot be further simplified, we can write √55 as √(5 * 11).
2. Simplifying √(1/55):
To simplify this, we need to rationalize the denominator. To do this, we multiply the numerator and the denominator by the conjugate of 55, which is 55 itself. By doing so, we get √(1/55) = √(1/55) * (√55/√55) = √55/55.
3. Simplifying √(5/11):
Similarly, we need to rationalize the denominator. Multiply the numerator and denominator by the conjugate of 11, which is also 11. We get √(5/11) = √(5/11) * (√11/√11) = √55/11.
Now, substitute these simplified expressions back into the given equation:
√55 - √(1/55) + √(5/11) = (√(5 * 11)) - (√55/55) + (√55/11)
Since all the denominators are the same, we can combine the fractions:
= (√(5 * 11) - √55 + √55) / 11
The second and third terms in the numerator will cancel out:
= (√(5 * 11) + √55) / 11
Finally, simplifying the expression:
= (√55 + √55) / 11
= (2√55) / 11
Therefore, the simplified form of the given expression is (2√55)/11.