SIMPLIFY 55/SQUARE ROOT OF 20 -3

To simplify the expression 55/square root of 20 - 3, we can follow these steps:

Step 1: Simplify the square root
The square root of 20 can be simplified by factoring it into its prime factors.

20 = 2 * 2 * 5

So, the square root of 20 is

√20 = √(2 * 2 * 5) = 2√5

Step 2: Rewrite the expression
Now that we have simplified the square root, we can rewrite the expression:

55 / (√20) - 3 = 55 / (2√5) - 3

Step 3: Rationalize the denominator
To rationalize the denominator (i.e., removing the square root from the denominator), we can multiply both the numerator and denominator by the conjugate of the denominator.

In this case, the conjugate of 2√5 is -2√5, so we can multiply both the numerator and denominator by -2√5:

[55 / (2√5)] * [-2√5 / -2√5] = -110√5 / (2√5 * 2√5) = -110√5 / 20

Step 4: Simplify the expression
Finally, we can simplify the resulting expression:

-110√5 / 20 = -11√5 / 2

Therefore, the simplified expression is -11√5 / 2.