Sure! Here’s a quick check on radicals and rational expressions. I’ll provide some sample questions and their solutions. You can try to solve them yourself first, and then look at the answers!
Sample Questions:
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Simplify the radical: \(\sqrt{72}\)
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Simplify the expression: \(\frac{3x^4y^2}{6xy}\)
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Rationalize the denominator: \(\frac{5}{\sqrt{2}}\)
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Combine the rational expressions: \(\frac{1}{x} + \frac{2}{x^2}\)
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Simplify the expression: \(\frac{\sqrt{50}}{\sqrt{2}}\)
Answers:
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Simplify the radical: \(\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}\)
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Simplify the expression: \(\frac{3x^4y^2}{6xy} = \frac{1}{2} x^{4-1}y^{2-1} = \frac{1}{2} x^3y\)
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Rationalize the denominator: \(\frac{5}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{5\sqrt{2}}{2}\)
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Combine the rational expressions: \(\frac{1}{x} + \frac{2}{x^2} = \frac{x + 2}{x^2}\)
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Simplify the expression: \(\frac{\sqrt{50}}{\sqrt{2}} = \sqrt{\frac{50}{2}} = \sqrt{25} = 5\)
Feel free to attempt these problems, and let me know if you have any questions or need further clarification!
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