I am racking my brain trying to figure out how to work this: the square root of 55 minus the square root of one over 55 plus the square root of 5 over 11. Do I use conjugates? Ahhhh!

use this abbreviation for square root. SQRT

so write the question as something like

sqrt(a)-sqrt(1/55) ....

I cannot follow your problem without ( _)

sqrt(55)-sqrt(1/55)+sqrt(5/11)=?

I understand that dealing with square roots and expressions involving them can be challenging. Let me break it down and guide you through solving the expression step by step.

To solve the expression: √55 - √(1/55) + √(5/11), we can use a combination of simplification techniques and a conjugate to eliminate radicals in the denominator. Here's how you can do it:

Step 1: Simplify the individual square roots.
√55 - √(1/55) + √(5/11)

√55 can't be simplified further since 55 doesn't have any perfect square factors.

For √(1/55):
Start by simplifying the fraction under the square root.
1/55 = 1 ÷ 55 = 0.01818 (approx)
The square root of 0.01818 is approximately 0.134 or 0.13383 (approx).

For √(5/11):
Simplify the fraction under the square root.
5/11 = 0.45454 (approx)
The square root of 0.45454 is approximately 0.674 or 0.67396 (approx).

Now we have: √55 - 0.134 + 0.674

Step 2: Combine like terms.
√55 - 0.134 + 0.674 = √55 + (0.674 - 0.134) = √55 + 0.54

We've simplified the expression to √55 + 0.54.

No need to introduce conjugates in this case. The final expression is √55 + 0.54.

If you need a numerical approximation, you can use a calculator to find the square root of 55 (approximately 7.416), then add 0.54 to it.

Remember, understanding how to simplify square roots and fractions can be helpful in solving more complex mathematical expressions.