\( \sqrt { 6.1 .4 \sqrt { 49 } + \sqrt[ 3 ] { - 8 } - ( - 4 ) ^ { 3 } } \)

Calculate or simplify the expression \( \sqrt{6.1*4*\sqrt{49}+\sqrt[3]{-8}-(-4)^3} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{6.1\times 4\sqrt{49}+\sqrt[3]{-8}-\left(-4\right)^{3}}\) - step1: Simplify the root: \(\sqrt{6.1\times 4\times 7+\sqrt[3]{-8}-\left(-4\right)^{3}}\) - step2: Simplify the root: \(\sqrt{6.1\times 4\times 7-2-\left(-4\right)^{3}}\) - step3: Multiply the terms: \(\sqrt{170.8-2-\left(-4\right)^{3}}\) - step4: Subtract the numbers: \(\sqrt{232.8}\) - step5: Rewrite the expression: \(\sqrt{\frac{1164}{5}}\) - step6: Use the properties of radicals: \(\frac{\sqrt{1164}}{\sqrt{5}}\) - step7: Simplify the expression: \(\frac{2\sqrt{291}}{\sqrt{5}}\) - step8: Multiply by the Conjugate: \(\frac{2\sqrt{291}\times \sqrt{5}}{\sqrt{5}\times \sqrt{5}}\) - step9: Multiply the numbers: \(\frac{2\sqrt{1455}}{\sqrt{5}\times \sqrt{5}}\) - step10: Multiply the numbers: \(\frac{2\sqrt{1455}}{5}\) The simplified form of the expression \( \sqrt{6.1*4*\sqrt{49}+\sqrt[3]{-8}-(-4)^3} \) is \( \frac{2\sqrt{1455}}{5} \) or approximately 15.257785.