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

Answer 1

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

\[ (5\sqrt{19})(6 - \sqrt{2}) = 5\sqrt{19} \cdot 6 - 5\sqrt{19} \cdot \sqrt{2} \]

Now, let's calculate each term:

1. \( 5\sqrt{19} \cdot 6 = 30\sqrt{19} \)
2. \( 5\sqrt{19} \cdot \sqrt{2} = 5\sqrt{38} \)

Putting it all together, we have:

\[ 30\sqrt{19} - 5\sqrt{38} \]

Thus, the exact answer is:

\[ 30\sqrt{19} - 5\sqrt{38} \]