multiply (5√19) (6√2) give an exact asnwer.

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

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

2. Multiply the square roots: \[ \sqrt{19} \times \sqrt{2} = \sqrt{19 \times 2} = \sqrt{38} \]

3. Combine the results: \[ (5\sqrt{19})(6\sqrt{2}) = 30\sqrt{38} \]

Thus, the exact answer is: \[ 30\sqrt{38} \]

To divide \( \frac{\sqrt{95}}{3\sqrt{5}} \), you can simplify the expression as follows:

1. Rewrite the expression: \[ \frac{\sqrt{95}}{3\sqrt{5}} = \frac{1}{3} \cdot \frac{\sqrt{95}}{\sqrt{5}} \]

2. Simplify the square roots: Use the property that \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \): \[ \frac{\sqrt{95}}{\sqrt{5}} = \sqrt{\frac{95}{5}} = \sqrt{19} \]

3. Combine the results: \[ \frac{\sqrt{95}}{3\sqrt{5}} = \frac{1}{3} \cdot \sqrt{19} = \frac{\sqrt{19}}{3} \]

Thus, the simplified result is: \[ \frac{\sqrt{19}}{3} \]

The exact answer for the division of \( \frac{\sqrt{95}}{3\sqrt{5}} \) is indeed \( \frac{\sqrt{19}}{3} \) as stated previously. Let's go through the steps to ensure clarity and confirm that it is in its exact form:

1. Original Expression: \[ \frac{\sqrt{95}}{3\sqrt{5}} \]

2. Separating the coefficient: \[ = \frac{1}{3} \cdot \frac{\sqrt{95}}{\sqrt{5}} \]

3. Using the property of square roots: \[ = \frac{1}{3} \cdot \sqrt{\frac{95}{5}} = \frac{1}{3} \cdot \sqrt{19} \]

4. Final Result: \[ = \frac{\sqrt{19}}{3} \]

So the exact answer is: \[ \frac{\sqrt{19}}{3} \]

This expression is in its simplest exact form.

To divide \( \frac{36\sqrt{39}}{9\sqrt{13}} \), follow these steps:

1. Separate the coefficients and the square roots: \[ \frac{36\sqrt{39}}{9\sqrt{13}} = \frac{36}{9} \cdot \frac{\sqrt{39}}{\sqrt{13}} \]

2. Simplify the coefficient: \[ \frac{36}{9} = 4 \]

3. Simplify the square roots: Use the property that \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \): \[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} = \sqrt{3} \]

4. Combine the results: \[ \frac{36\sqrt{39}}{9\sqrt{13}} = 4 \cdot \sqrt{3} = 4\sqrt{3} \]

Thus, the exact answer is: \[ 4\sqrt{3} \]

To simplify \(\sqrt{48}\), follow these steps:

1. Factor the number under the square root: \[ 48 = 16 \times 3 \]

2. Use the property of square roots: \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} \]

3. Simplify: \[ \sqrt{16} = 4 \] So, \[ \sqrt{48} = 4 \times \sqrt{3} = 4\sqrt{3} \]

Therefore, the simplified form of \(\sqrt{48}\) is: \[ 4\sqrt{3} \]

To simplify \( 3\sqrt{54} \), follow these steps:

1. Factor the number under the square root: \[ 54 = 9 \times 6 \]

2. Use the property of square roots: \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} \]

3. Simplify: \[ \sqrt{9} = 3 \] So, \[ \sqrt{54} = 3\sqrt{6} \]

4. Now, multiply by the coefficient (3): \[ 3\sqrt{54} = 3 \cdot 3\sqrt{6} = 9\sqrt{6} \]

Therefore, the simplified form of \( 3\sqrt{54} \) is: \[ 9\sqrt{6} \]