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Rewrite the radical by extracting all possible roots and write your answer in radical form 75x4y7−−−−−−√

User Bvpb
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1 Answer

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Answer:


√(75x^4y^7) = 5x^2y^3√(3y)

Explanation:

Given


\sqrt{75x^4y^7

Required

Rewrite

Express 75 as 25 * 3


√(75x^4y^7) = √(25 * 3x^4y^7)

Split


√(75x^4y^7) = √(25) * √(3x^4y^7)

This gives:


√(75x^4y^7) = 5 * √(3x^4y^7)

Express y^7 as y^6 * y


√(75x^4y^7) = 5 * √(3*x^4 * y^6 * y)

Split


√(75x^4y^7) = 5 * √(3) *√(x^4) * √(y^6) * √(y)

Express square roots as exponents


√(75x^4y^7) = 5 * √(3) * x^{(4 * (1)/(2))} * y^{(6* (1)/(2))} * √(y)


√(75x^4y^7) = 5 * √(3) * x^2 * y^3 * √(y)

Rewrite the factors


√(75x^4y^7) = 5 * x^2 * y^3* √(3) * √(y)


√(75x^4y^7) = 5x^2y^3* √(3) * √(y)

Combine roots


√(75x^4y^7) = 5x^2y^3* √(3y)


√(75x^4y^7) = 5x^2y^3√(3y)

User BgRva
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