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[tex] \sqrt{ \sqrt{49 \times 7} } \\ = \sqrt{7 \sqrt{7} } \\ = {7}^{ \frac{1}{2} } \times \sqrt{ {7}^{ \frac{1}{2} } } \\ = {7}^{ \frac{1}{2} } \times {7}^{ \frac{1}{4} } \\ = {7}^{ \frac{3}{4} } [/tex]

devishri1977

Answer:

Step-by-step explanation:

[tex]\sqrt{\sqrt{49*7}}=\sqrt{\sqrt{7*7*7}}\\\\=\sqrt{\sqrt{7^{3}}}\\\\=\sqrt{(7^{3})^{\frac{1}{2}}}\\\\=\sqrt{7^{\frac{3}{2}}}\\\\ =(7^{\frac{3}{2}})^{\frac{1}{2}\\\\=7^{\frac{3}{4}}=(7^{3})^{\frac{1}{4}}\\\\=\sqrt[4]{7^{3}}=\sqrt[n]{7*7*7}\\\\=\sqrt[4]{343}[/tex]

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