Multiply (5 −−−√ 19) (6–√2) . Give an exact answer.(1 point)

Answer 1

To multiply the expressions \( (5 - \sqrt{19})(6 - \sqrt{2}) \), we can use the distributive property (also known as the FOIL method for binomials).

Let's multiply them step by step:

1. Multiply the first terms: \[ 5 \times 6 = 30 \]

2. Multiply the outer terms: \[ 5 \times (-\sqrt{2}) = -5\sqrt{2} \]

3. Multiply the inner terms: \[ -\sqrt{19} \times 6 = -6\sqrt{19} \]

4. Multiply the last terms: \[ -\sqrt{19} \times (-\sqrt{2}) = \sqrt{19} \cdot \sqrt{2} = \sqrt{38} \]

Now, we combine all these results: \[ 30 - 5\sqrt{2} - 6\sqrt{19} + \sqrt{38} \]

The exact answer is: \[ 30 - 5\sqrt{2} - 6\sqrt{19} + \sqrt{38} \]