Question

Subtract 11 square root 19 - 5 square root 19. (1 point)
The difference is

Answer 1

Multiply (5sqrt19 ) (6sqrt2). Give an exact answer. (1 point)

Answer 2

To subtract \(11 \sqrt{19} - 5 \sqrt{19}\), you can combine the like terms since both terms involve \(\sqrt{19}\).

\[
11 \sqrt{19} - 5 \sqrt{19} = (11 - 5) \sqrt{19} = 6 \sqrt{19}
\]

So, the difference is \(6 \sqrt{19}\).

Answer 3

To multiply \( (5\sqrt{19}) \) and \( (6\sqrt{2}) \), you can multiply the coefficients (5 and 6) and then multiply the square roots:

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

\[
= 30 \cdot \sqrt{19 \cdot 2}
\]

Now, simplify the square root:

\[
= 30 \cdot \sqrt{38}
\]

Thus, the exact answer is

\[
30\sqrt{38}
\]