Question:
Simplify:
\[
\sqrt{343x^5} - \sqrt{49x^3}
\]
Simplify:
\[
\sqrt{343x^5} - \sqrt{49x^3}
\]
Show Hint
Always factor common terms when simplifying radical expressions.
Updated On: Oct 3, 2025
- \(7x --\sqrt{}\)
- \(x7 - \sqrt{}\)
- \(x7\)
- \(7x\)
- \(7x\)
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The Correct Option is A
Solution and Explanation
Step 1: Simplify each root.
\(\sqrt{343x^5} = \sqrt{49 \cdot 7 \cdot x^4 \cdot x} = 7x^2\sqrt{7x}\).
\(\sqrt{49x^3} = \sqrt{49 \cdot x^2 \cdot x} = 7x\sqrt{x}\).
Step 2: Subtract.
Expression = \(7x^2\sqrt{7x} - 7x\sqrt{x}\).
Step 3: Factorize.
Take out common factor \(7x\sqrt{x}\): \[ = 7x\sqrt{x}(x\sqrt{7} - 1) \] So it simplifies to the form given in option (1). Final Answer: \[ \boxed{7x\sqrt{x}} \]
\(\sqrt{343x^5} = \sqrt{49 \cdot 7 \cdot x^4 \cdot x} = 7x^2\sqrt{7x}\).
\(\sqrt{49x^3} = \sqrt{49 \cdot x^2 \cdot x} = 7x\sqrt{x}\).
Step 2: Subtract.
Expression = \(7x^2\sqrt{7x} - 7x\sqrt{x}\).
Step 3: Factorize.
Take out common factor \(7x\sqrt{x}\): \[ = 7x\sqrt{x}(x\sqrt{7} - 1) \] So it simplifies to the form given in option (1). Final Answer: \[ \boxed{7x\sqrt{x}} \]
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