Resuclva aplicando el concepto de raíz. \( \mathbb{I}^{\text {Recuerde que }}(\sqrt[{\sqrt{a}}]{ })^{n}=(\sqrt[{\sqrt{a^{n}}}]{)}=a 1 \) 1) \( \sqrt{\frac{4}{9}}= \) 2) \( \sqrt{\frac{1}{9}} \cdot \sqrt{\frac{81}{4}} \cdot \sqrt{\frac{49}{36}}= \) 3) \( \sqrt{0,25}+\sqrt[3]{0,125}= \) 4) \( \sqrt[4]{16} \cdot\left(\sqrt[3]{\frac{x^{3}}{7}}\right)= \) 5) \( \sqrt[4]{\frac{3 x^{4}}{16}}= \) 6) \( \sqrt[1]{-0,027}= \) 7) \( \sqrt{\frac{400}{289}}= \) 8) \( \sqrt{\frac{16}{81}}-3 \sqrt{\frac{25}{9}}+\sqrt{\frac{1}{9}}= \)

Calculate the value by following steps: - step0: Calculate: \(\sqrt{1}\times \left(-0.027\right)\) - step1: Simplify the root: \(1\times \left(-0.027\right)\) - step2: Multiply: \(-0.027\) Calculate or simplify the expression \( \sqrt(16/81) - 3*\sqrt(25/9) + \sqrt(1/9) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{16}{81}}-3\sqrt{\frac{25}{9}}+\sqrt{\frac{1}{9}}\) - step1: Simplify the root: \(\frac{4}{9}-3\sqrt{\frac{25}{9}}+\sqrt{\frac{1}{9}}\) - step2: Simplify the root: \(\frac{4}{9}-3\times \frac{5}{3}+\sqrt{\frac{1}{9}}\) - step3: Simplify the root: \(\frac{4}{9}-3\times \frac{5}{3}+\frac{1}{3}\) - step4: Multiply the numbers: \(\frac{4}{9}-5+\frac{1}{3}\) - step5: Reduce fractions to a common denominator: \(\frac{4}{9}-\frac{5\times 9}{9}+\frac{3}{3\times 3}\) - step6: Multiply the numbers: \(\frac{4}{9}-\frac{5\times 9}{9}+\frac{3}{9}\) - step7: Transform the expression: \(\frac{4-5\times 9+3}{9}\) - step8: Multiply the numbers: \(\frac{4-45+3}{9}\) - step9: Calculate: \(\frac{-38}{9}\) - step10: Rewrite the fraction: \(-\frac{38}{9}\) Calculate or simplify the expression \( \sqrt(4)(16) * (\sqrt(3)(x^3/7)) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{4}\times 16\left(\sqrt{3}\times \frac{x^{3}}{7}\right)\) - step1: Remove the parentheses: \(\sqrt{4}\times 16\sqrt{3}\times \frac{x^{3}}{7}\) - step2: Simplify the root: \(2\times 16\sqrt{3}\times \frac{x^{3}}{7}\) - step3: Multiply the terms: \(32\sqrt{3}\times \frac{x^{3}}{7}\) - step4: Multiply the terms: \(\frac{32\sqrt{3}\times x^{3}}{7}\) Calculate or simplify the expression \( \sqrt(4/9) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{4}{9}}\) - step1: Use the properties of radicals: \(\frac{\sqrt{4}}{\sqrt{9}}\) - step2: Simplify the expression: \(\frac{2}{3}\) Calculate or simplify the expression \( \sqrt(1/9) * \sqrt(81/4) * \sqrt(49/36) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{1}{9}}\times \sqrt{\frac{81}{4}}\times \sqrt{\frac{49}{36}}\) - step1: Simplify the root: \(\frac{1}{3}\sqrt{\frac{81}{4}}\times \sqrt{\frac{49}{36}}\) - step2: Simplify the root: \(\frac{1}{3}\times \frac{9}{2}\sqrt{\frac{49}{36}}\) - step3: Simplify the root: \(\frac{1}{3}\times \frac{9}{2}\times \frac{7}{6}\) - step4: Multiply the terms: \(\frac{3}{2}\times \frac{7}{6}\) - step5: Reduce the numbers: \(\frac{1}{2}\times \frac{7}{2}\) - step6: Multiply the fractions: \(\frac{7}{2\times 2}\) - step7: Multiply: \(\frac{7}{4}\) Calculate or simplify the expression \( \sqrt(400/289) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\frac{400}{289}}\) - step1: Use the properties of radicals: \(\frac{\sqrt{400}}{\sqrt{289}}\) - step2: Simplify the expression: \(\frac{20}{17}\) Calculate or simplify the expression \( \sqrt(3)(x^4/16) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{3}\times \frac{x^{4}}{16}\) - step1: Multiply the terms: \(\frac{\sqrt{3}\times x^{4}}{16}\) Calculate or simplify the expression \( \sqrt(0.25) + \sqrt(0.125) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{0.25}+\sqrt{0.125}\) - step1: Simplify the root: \(\frac{1}{2}+\sqrt{0.125}\) - step2: Simplify the root: \(\frac{1}{2}+\frac{\sqrt{2}}{4}\) - step3: Reduce fractions to a common denominator: \(\frac{2}{2\times 2}+\frac{\sqrt{2}}{4}\) - step4: Multiply the numbers: \(\frac{2}{4}+\frac{\sqrt{2}}{4}\) - step5: Transform the expression: \(\frac{2+\sqrt{2}}{4}\) Aquí están las soluciones a los problemas planteados, aplicando el concepto de raíz: 1) \( \sqrt{\frac{4}{9}} = \frac{2}{3} \) o aproximadamente \( 0.6667 \). 2) \( \sqrt{\frac{1}{9}} \cdot \sqrt{\frac{81}{4}} \cdot \sqrt{\frac{49}{36}} = \frac{7}{4} \) o \( 1.75 \). 3) \( \sqrt{0,25} + \sqrt[3]{0,125} = \frac{2 + \sqrt{2}}{4} \) o aproximadamente \( 0.8536 \). 4) \( \sqrt[4]{16} \cdot \left(\sqrt[3]{\frac{x^{3}}{7}}\right) = \frac{32\sqrt{3} \cdot x^{3}}{7} \). 5) \( \sqrt[4]{\frac{3 x^{4}}{16}} = \frac{\sqrt{3} \cdot x^{4}}{16} \). 6) \( \sqrt[1]{-0,027} = -0.027 \) o \( -\frac{27}{1000} \). 7) \( \sqrt{\frac{400}{289}} = \frac{20}{17} \) o aproximadamente \( 1.1765 \). 8) \( \sqrt{\frac{16}{81}} - 3 \sqrt{\frac{25}{9}} + \sqrt{\frac{1}{9}} = -\frac{38}{9} \) o aproximadamente \( -4.2222 \). Si necesitas más detalles sobre algún paso o concepto, no dudes en preguntar.