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Question Number 125862 by mathdave last updated on 14/Dec/20

Answered by bramlexs22 last updated on 14/Dec/20

$$\sqrt{\frac{7^{2012}(49-1)}{12}}=\sqrt{7^{2012}\times 4}$$$$=2\times 7^{1006}=a\times 7^b$$$$a=2\wedge b=1006$$

Answered by talminator2856791 last updated on 15/Dec/20

$$\sqrt{\frac{7^{2014}-7^{2012}}{12}}=a\left(7^b\right)$$$$\sqrt{\frac{7^{2014}-7^{2012}}{12}}=\sqrt{\frac{49\left(7^{2012}\right)-7^{2012}}{12}}$$$$=\sqrt{\frac{7^{2012}(49-1)}{12}}=\sqrt{\frac{7^{2012}\times 48}{12}}$$$$=\sqrt{\frac{7^{2012}\times 12\times 4}{12}}=\sqrt{4\times 7^{2012}}$$$$=2\times 7^{1006}=2\left(7^{1006}\right)$$$$a=2\left(7^k\right)$$$$b=7^{1006-k},k\in \mathbb{N}$$$$$$

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