Radical Time.. :D

I simply broke up everything into 2s In the numerator, you get 2^32 + 2^12 and in the denom, you get 2^8 + 2^28. Factoring, you get ((2^12)(2^20 +1))/((2^8)(2^20 + 1)) (2^20 + 1) cancels out 2^12 / 2^ 8 = 2^4 (2^4 )^0.5 = 2^2 =4

Let x = 16

the expression will be:

√[(x^8 + x^3)/(x^2 + x^7)

= √[(x^2)(x^6 + x)/(x^2)(1 + x^5)

= √[(x)(x^5 + 1)/(x^5 + 1)]

= √x

= √16

= 4

Final answer: 4

Break up everything into powers of 2: $\sqrt{\frac{2^{32}+2^{12}}{2^8+2^{28}}}$ \sqrt{\frac{2^{12}(2^{20}+1)}{2^8{1+2^{20}}} $\frac{\sqrt{2^{12}}\sqrt{2^{20}+1}}{\sqrt{2^8}\sqrt{1+2^{20}}}$ The $\sqrt{2^{20}+1}$ s get cancelled and only $\frac{\sqrt{2^{12}}}{\sqrt{2^8}}$ remains which gets simplified as follows: $\frac{2^6}{2^4}$ $2^{6-4}$ $2^2=4$ So the answer is $\large{4}$

8^4 = 16^3.

Now take 16 out in the numerator. Numerator and denominator cancels and we are left with √16=4

simply 8^4 = 16^3 then factor out the lowest exponents and you will get the square root of [16^3 (16^5 +1)] / [16^2 (1 + 16^5) common factors cancels out, you get the square root of 16, which is equal to 4

Answer=sqrt((16^8+8^4)/(16^2+16^7))=4

=((2^32+2^12)/(2^8+2^28))^0.5 =((2^12 * (1+2^20))/(2^8(1+2^20)))^0.5 =(2^12/2^8)^0.5 =(2^4)^0.5 =4

(16^4(16^4+(0.5^4)*16^4)/16^4((1/16^2)+16^3))^0.5=(16)^0.5

8^4=16^3 so 16^3(16^5 +1)/(16^2(1+16^5)) = 16 so sqrt(16)=4

okay! what if we take logarithm of base 16 and then solve it. its giving 16^5 as answer???