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

Sagot :

MrRoyalidn

Answer:

[tex]\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{75x^4y^7[/tex]

Required

Rewrite

Express 75 as 25 * 3

[tex]\sqrt{75x^4y^7} = \sqrt{25 * 3x^4y^7}[/tex]

Split

[tex]\sqrt{75x^4y^7} = \sqrt{25} * \sqrt{3x^4y^7}[/tex]

This gives:

[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3x^4y^7}[/tex]

Express y^7 as y^6 * y

[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3*x^4 * y^6 * y}[/tex]

Split

[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} *\sqrt{x^4} * \sqrt{y^6} * \sqrt{y}[/tex]

Express square roots as exponents

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

[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^2 * y^3 * \sqrt{y}[/tex]

Rewrite the factors

[tex]\sqrt{75x^4y^7} = 5 * x^2 * y^3* \sqrt{3} * \sqrt{y}[/tex]

[tex]\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3} * \sqrt{y}[/tex]

Combine roots

[tex]\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3y}[/tex]

[tex]\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}[/tex]

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