Question

Introduce en los radicales los factores que están fuera de ellos

\frac{16}{3} . \sqrt{a}

-7. 11^{3} . \sqrt{2a}

\frac{1}{4} .b. \sqrt{ 3^{3} b^{3} }

a^{2}.b. \sqrt[3]{3b}

Answer 1

$\star \ \frac{16}{3} . \sqrt{a} = \sqrt{(\frac{16}{3})^2}. \sqrt{a} \\ \\ \frac{16}{3} . \sqrt{a} = \sqrt{(\frac{256}{9})}. \sqrt{a} \\ \\ \frac{16}{3} . \sqrt{a} = \sqrt{\frac{256}{9}a}$
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$\star\ -7. 11^{3} . \sqrt{2a} = -( \sqrt{(7.11^3)^2 )}. \sqrt{2a} \\ \\ -7. 11^{3} . \sqrt{2a} = -( \sqrt{(7^2.11^6)}). \sqrt{2a} \\ \\ -7. 11^{3} . \sqrt{2a} = -( \sqrt{(49.1771561}). \sqrt{2a} \\ \\ -7. 11^{3} . \sqrt{2a} = -( \sqrt{86806489}). \sqrt{2a} \\ \\ -7. 11^{3} . \sqrt{2a} = -( \sqrt{(86806489).2a}) \\ \\ -7. 11^{3} . \sqrt{2a} = - \sqrt{173612978a}$
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$\star \ \frac{1}{4} .b. \sqrt{ 3^{3} b^{3} } = \sqrt{(\frac{1}{4}b)^2}. \sqrt{ 3^{3} b^{3} } \\ \\ \frac{1}{4} .b. \sqrt{ 3^{3} b^{3} } = \sqrt{\frac{1}{16}b^2}. \sqrt{ 27 b^{3} } \\ \\ \frac{1}{4} .b. \sqrt{ 3^{3} b^{3} } = \sqrt{\frac{1}{16}b^2.27b^3} \\ \\ \frac{1}{4} .b. \sqrt{ 3^{3} b^{3} } = \sqrt{\frac{27}{16}b^5}$
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$\star \ a^{2}.b. \sqrt[3]{3b}= \sqrt[3]{(a^2b)^3}. \sqrt[3]{3b} \\ \\ a^{2}.b. \sqrt[3]{3b}= \sqrt[3]{a^6b^3}. \sqrt[3]{3b} \\ \\ a^{2}.b. \sqrt[3]{3b}= \sqrt[3]{a^6b^3.3b}\\ \\ a^{2}.b. \sqrt[3]{3b}= \sqrt[3]{3a^6b^4}$


Espero que te sirva, salu2!!!!