-2 - radical bar 5 over

radical bar 10

simplify

To simplify the expression -2 - √(5/√10), let's break it down step by step:

Step 1: Simplify the radicals individually.
√10 is an irrational number, so we can't simplify it further.
√(5/√10) can be simplified by rationalizing the denominator. To do this, multiply the numerator and denominator by the conjugate of √10, which is √10:
√(5/√10) = √(5/√10) * (√10/√10) = (√50/10) = √50/10

Step 2: Combine like terms.
The expression -2 - √(5/√10) becomes -2 - √50/10.

Step 3: Further simplify the radical.
√50 can be simplified by factoring it: √(25 * 2) = √25 * √2 = 5√2.
Therefore, √50/10 = 5√2/10.

Step 4: Simplify the coefficient.
5√2/10 can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 5:
5√2/10 = (5/5) * √2/2 = 1/2 * √2.

Thus, the simplified expression of -2 - √(5/√10) is -2 - 1/2 * √2.