To match the radicals with their simplified versions, let's simplify each radical expression step by step:
-
Simplifying \( \sqrt{18x^5y^3} \):
- \( 18 = 9 \times 2 = 3^2 \times 2 \), so \( \sqrt{18} = 3\sqrt{2} \).
- For \( x^5 \), \( \sqrt{x^5} = x^2\sqrt{x} \).
- For \( y^3 \), \( \sqrt{y^3} = y\sqrt{y} \).
- Therefore, \( \sqrt{18x^5y^3} = 3\sqrt{2} \cdot x^2 \sqrt{x} \cdot y\sqrt{y} = 3x^2y\sqrt{2xy} \).
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Simplifying \( \sqrt{98x^5y} \):
- \( 98 = 49 \times 2 = 7^2 \times 2 \), so \( \sqrt{98} = 7\sqrt{2} \).
- For \( x^5 \), \( \sqrt{x^5} = x^2\sqrt{x} \).
- For \( y \), \( \sqrt{y} = \sqrt{y} \).
- Therefore, \( \sqrt{98x^5y} = 7\sqrt{2} \cdot x^2 \sqrt{x} \cdot \sqrt{y} = 7x^2\sqrt{2xy} \).
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Simplifying \( \sqrt{9x^2} \):
- \( \sqrt{9} = 3 \).
- \( \sqrt{x^2} = x \).
- Therefore, \( \sqrt{9x^2} = 3x \).
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Simplifying \( \sqrt{49x^3y^4} \):
- \( \sqrt{49} = 7 \).
- For \( x^3 \), \( \sqrt{x^3} = x\sqrt{x} \).
- For \( y^4 \), \( \sqrt{y^4} = y^2 \).
- Therefore, \( \sqrt{49x^3y^4} = 7 \cdot x\sqrt{x} \cdot y^2 = 7y^2x\sqrt{x} \).
Now let's match the simplified versions to their corresponding radicals:
- \( \sqrt{18x^5y^3} \) matches with \( 3x^2y\sqrt{2xy} \) (none provided).
- \( \sqrt{98x^5y} \) matches with \( 7x^2\sqrt{2xy} \) (none provided).
- \( \sqrt{9x^2} \) matches with \( 3x \).
- \( \sqrt{49x^3y^4} \) matches with \( 7y^2x\sqrt{x} \).
Final matching based on provided responses would lead to:
- Eventual matches may not show exact matched forms.
- If instructions are provided to insert or correlate directly, you may input the matches based on the simplified outputs as visible.
Please confirm, or check the solutions thoroughly against simplified forms.