Let's solve the problems one by one:
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Add \( \sqrt{510} + \sqrt{10} \)
To simplify, we can evaluate \( \sqrt{510} \): \[ 510 = 51 \times 10 = 51 \times (5 \times 2) \] While it doesn't simplify to an integer or simple square root directly, we can express it in simpler radical form:
\( \sqrt{510} = \sqrt{51} \sqrt{10} \)
So, \[ \sqrt{510} + \sqrt{10} = \sqrt{10}(\sqrt{51}+1) \] However, since we consider the options: None of the options seem to directly apply, but \( \sqrt{60} \) could be a possible interpretation if you misunderstood the values or options.
Therefore, the simplified sum form does not provide a clear answer unless further clarification is provided.
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Subtract \( 11\sqrt{19} - 5\sqrt{19} \)
\[ 11\sqrt{19} - 5\sqrt{19} = (11 - 5)\sqrt{19} = 6\sqrt{19} \] The difference is \( 6\sqrt{19} \).
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Multiply \( (5\sqrt{19})(6\sqrt{2}) \)
\[ (5\sqrt{19})(6\sqrt{2}) = 30\sqrt{38} \] So, the result is \( 30\sqrt{38} \).
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Divide \( \frac{\sqrt{95}}{3\sqrt{5}} \)
To divide, we can simplify: \[ \frac{\sqrt{95}}{3\sqrt{5}} = \frac{\sqrt{19 \times 5}}{3\sqrt{5}} = \frac{\sqrt{19}\sqrt{5}}{3\sqrt{5}} = \frac{\sqrt{19}}{3} \] So, the exact answer is \( \frac{\sqrt{19}}{3} \).
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Divide \( \frac{36\sqrt{39}}{9\sqrt{13}} \)
Simplifying the expression: \[ \frac{36\sqrt{39}}{9\sqrt{13}} = 4\frac{\sqrt{39}}{\sqrt{13}} = 4\sqrt{\frac{39}{13}} = 4\sqrt{3} \] So, the exact answer is \( 4\sqrt{3} \).
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Simplify \( \sqrt{48} \)
\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \] So, it simplifies to \( 4\sqrt{3} \).
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Simplify \( \sqrt[3]{54} \)
\[ \sqrt[3]{54} = \sqrt[3]{27 \times 2} = \sqrt[3]{27} \cdot \sqrt[3]{2} = 3\sqrt[3]{2} \] So, it simplifies to \( 3\sqrt[3]{2} \).
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Rewrite \( \sqrt{63} \)
\[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7} \] So, it can be rewritten as \( 3\sqrt{7} \).
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Rewrite \( \sqrt[3]{81} \)
\[ \sqrt[3]{81} = \sqrt[3]{27 \times 3} = \sqrt[3]{27}\cdot\sqrt[3]{3} = 3\sqrt[3]{3} \] So, it can be rewritten as \( 3\sqrt[3]{3} \).
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Find the square root of 169
\[ \sqrt{169} = 13 \quad (\text{and also } -13) \] So, the response is \( 13, -13 \).
If you have additional questions or need further assistance, feel free to ask!