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![\sqrt[3]{ \sqrt[3]{216} + \sqrt[3]{1000} + \sqrt[3]{1331} } \\ \\ = \sqrt[3]{ \sqrt[3]{ {6}^{3} } + \sqrt[3]{ {10}^{3} } + \sqrt[3]{ {11}^{3} } } \\ \\ = \sqrt[3]{6 + 10 + 11} \\ \\ = \sqrt[3]{27} = \sqrt[3]{ {3}^{3} } \\ \\ = 3 \\ \\ \Rightarrow \: \: \: \: \: \:\boxed{ \mathbf{Ans :3} }](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B++%5Csqrt%5B3%5D%7B216%7D+%2B++%5Csqrt%5B3%5D%7B1000%7D++++%2B++%5Csqrt%5B3%5D%7B1331%7D+%7D++%5C%5C++%5C%5C++%3D++%5Csqrt%5B3%5D%7B+%5Csqrt%5B3%5D%7B+%7B6%7D%5E%7B3%7D+%7D++%2B++%5Csqrt%5B3%5D%7B+%7B10%7D%5E%7B3%7D+%7D+%2B++%5Csqrt%5B3%5D%7B+%7B11%7D%5E%7B3%7D+%7D++%7D++%5C%5C++%5C%5C++%3D+++%5Csqrt%5B3%5D%7B6+%2B+10+%2B+11%7D++%5C%5C++%5C%5C++%3D++%5Csqrt%5B3%5D%7B27%7D++%3D++%5Csqrt%5B3%5D%7B+%7B3%7D%5E%7B3%7D+%7D++%5C%5C++%5C%5C++%3D+3++%5C%5C+++%5C%5C++%5CRightarrow+%5C%3A+%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A%5Cboxed%7B+%5Cmathbf%7BAns+%3A3%7D+%7D+ "\sqrt[3]{ \sqrt[3]{216} + \sqrt[3]{1000} + \sqrt[3]{1331} } \\ \\ = \sqrt[3]{ \sqrt[3]{ {6}^{3} } + \sqrt[3]{ {10}^{3} } + \sqrt[3]{ {11}^{3} } } \\ \\ = \sqrt[3]{6 + 10 + 11} \\ \\ = \sqrt[3]{27} = \sqrt[3]{ {3}^{3} } \\ \\ = 3 \\ \\ \Rightarrow \: \: \: \: \: \:\boxed{ \mathbf{Ans :3} }")
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Good morning
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Your answer is given in the attachment
I hope it will help you a lot
Thanks
Have a nice day
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