Number system

What is the positive square root of $31+4\sqrt{57}$?

If N =$\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}$ , then what is the value of N + $\frac{1}{N}$?

If $\frac{\sqrt{2+x}+\sqrt{2-x}}{\sqrt{2+x}-\sqrt{2-x}}=2$, the what is value of x?

$\text{What is the value of }\left(\frac{3^n+3^n{}^{-1}}{3^{n+1}-3^n}\right)?$

What is the value of a, if log_a 4 + log_a 16 + log_a 64 + log_a 256 = 10?

What is the value of log₅ 10 × log₁₀ 15 × log₁₅ 20 × log₂₀ 25?

What is the value of x, if 0.01^x = 2?

What is the value of log₁₀ 10 + log₁₀ 10² + ………+ log₁₀ 10ⁿ?

What is the remainder when 6729 is divided by 35?

On dividing a certain number by 357, the remainder is 39. On dividing the same number by 17, what will be the remainder?