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bezimeni [28]
3 years ago
15

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

Mathematics
1 answer:
attashe74 [19]3 years ago
7 0

Answer:

\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}

Step-by-step explanation:

Given

\sqrt{75x^4y^7

Required

Rewrite

Express 75 as 25 * 3

\sqrt{75x^4y^7} = \sqrt{25 * 3x^4y^7}

Split

\sqrt{75x^4y^7} = \sqrt{25} * \sqrt{3x^4y^7}

This gives:

\sqrt{75x^4y^7} = 5 * \sqrt{3x^4y^7}

Express y^7 as y^6 * y

\sqrt{75x^4y^7} = 5 * \sqrt{3*x^4 * y^6 * y}

Split

\sqrt{75x^4y^7} = 5 * \sqrt{3} *\sqrt{x^4} * \sqrt{y^6} * \sqrt{y}

Express square roots as exponents

\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^{(4 * \frac{1}{2})} * y^{(6* \frac{1}{2})} * \sqrt{y}

\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^2 * y^3 * \sqrt{y}

Rewrite the factors

\sqrt{75x^4y^7} = 5  * x^2 * y^3* \sqrt{3} * \sqrt{y}

\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3} * \sqrt{y}

Combine roots

\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3y}

\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}

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