QuestionAugust 24, 2025

Which expression is equivalent to sqrt (98x^8y^5z^40) in lowest terms? 49x^6y^3z^38 49x^4y^2z^20sqrt (y) 7x^6y^3z^38sqrt (2) 7x^4y^2z^20sqrt (2y)

Which expression is equivalent to sqrt (98x^8y^5z^40) in lowest terms? 49x^6y^3z^38 49x^4y^2z^20sqrt (y) 7x^6y^3z^38sqrt (2) 7x^4y^2z^20sqrt (2y)
Which expression is equivalent to sqrt (98x^8y^5z^40) in lowest terms?
49x^6y^3z^38
49x^4y^2z^20sqrt (y)
7x^6y^3z^38sqrt (2)
7x^4y^2z^20sqrt (2y)

Solution
3.4(221 votes)

Answer

7x^{4}y^{2}z^{20}\sqrt{2y} Explanation 1. Simplify the square root Break down \sqrt{98x^8y^5z^{40}} into simpler parts: \sqrt{98} \cdot \sqrt{x^8} \cdot \sqrt{y^5} \cdot \sqrt{z^{40}}. 2. Simplify each component \sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}, \sqrt{x^8} = x^4, \sqrt{y^5} = y^2\sqrt{y}, \sqrt{z^{40}} = z^{20}. 3. Combine simplified components Combine all parts: 7x^4y^2z^{20}\sqrt{2y}.

Explanation

1. Simplify the square root<br /> Break down $\sqrt{98x^8y^5z^{40}}$ into simpler parts: $\sqrt{98} \cdot \sqrt{x^8} \cdot \sqrt{y^5} \cdot \sqrt{z^{40}}$.<br />2. Simplify each component<br /> $\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}$, $\sqrt{x^8} = x^4$, $\sqrt{y^5} = y^2\sqrt{y}$, $\sqrt{z^{40}} = z^{20}$.<br />3. Combine simplified components<br /> Combine all parts: $7x^4y^2z^{20}\sqrt{2y}$.
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