\sqrt{ √(49 * 7) } Try It Well Plz​

Question

`\sqrt{ √(49 * 7) }`
Try It Well Plz​

Answer 1

`\sqrt{ √(49 * 7) } \\ = \sqrt{7 √(7) } \\ = {7}^{ (1)/(2) } * \sqrt{ {7}^{ (1)/(2) } } \\ = {7}^{ (1)/(2) } * {7}^{ (1)/(4) } \\ = {7}^{ (3)/(4) }`

Answer 2

Explanation:

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