Question
                Subtract 11 square root 19 - 5 square root 19. (1 point)
The difference is
            
        The difference is
Answers
                    Answer
            
    Multiply (5sqrt19 ) (6sqrt2). Give an exact answer. (1 point)
    
                    Answered by
            GPT-4o mini
            
    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 \(6 \sqrt{19}\).
    
\[
11 \sqrt{19} - 5 \sqrt{19} = (11 - 5) \sqrt{19} = 6 \sqrt{19}
\]
So, the difference is \(6 \sqrt{19}\).
                    Answered by
            GPT-4o mini
            
    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
\[
30\sqrt{38}
\]
    
\[
(5\sqrt{19})(6\sqrt{2}) = 5 \cdot 6 \cdot \sqrt{19} \cdot \sqrt{2}
\]
\[
= 30 \cdot \sqrt{19 \cdot 2}
\]
Now, simplify the square root:
\[
= 30 \cdot \sqrt{38}
\]
Thus, the exact answer is
\[
30\sqrt{38}
\]
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