QuestionAugust 26, 2025

Simplify the radical below. 7sqrt (200x^5y^8) square

Simplify the radical below. 7sqrt (200x^5y^8) square
Simplify the radical below. 7sqrt (200x^5y^8) square

Solution
4.7(170 votes)

Answer

35x^2y^4\sqrt{2x} Explanation 1. Simplify the radical expression Break down 200x^5y^8 into prime factors: 200 = 2^3 \times 5^2, x^5 = x^4 \times x, and y^8 = y^8. 2. Apply square root to each factor Use \sqrt{a^2} = a: \sqrt{200x^5y^8} = \sqrt{2^3 \times 5^2 \times x^4 \times x \times y^8}. Simplify: \sqrt{2^3} = 2\sqrt{2}, \sqrt{5^2} = 5, \sqrt{x^4} = x^2, \sqrt{x} = \sqrt{x}, \sqrt{y^8} = y^4. 3. Combine simplified terms Combine: 7 \times 5 \times x^2 \times y^4 \times \sqrt{2x} = 35x^2y^4\sqrt{2x}.

Explanation

1. Simplify the radical expression<br /> Break down $200x^5y^8$ into prime factors: $200 = 2^3 \times 5^2$, $x^5 = x^4 \times x$, and $y^8 = y^8$. <br />2. Apply square root to each factor<br /> Use $\sqrt{a^2} = a$: $\sqrt{200x^5y^8} = \sqrt{2^3 \times 5^2 \times x^4 \times x \times y^8}$.<br /> Simplify: $\sqrt{2^3} = 2\sqrt{2}$, $\sqrt{5^2} = 5$, $\sqrt{x^4} = x^2$, $\sqrt{x} = \sqrt{x}$, $\sqrt{y^8} = y^4$.<br />3. Combine simplified terms<br /> Combine: $7 \times 5 \times x^2 \times y^4 \times \sqrt{2x} = 35x^2y^4\sqrt{2x}$.
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