\(The expression \sqrt{(\sqrt{56})(\sqrt{126})} can be simplified to a\sqrt b, where a and b are integers and b is not divisible by any perfect square greater than 1. What is a+b?\)
+1008 Sorry, this is very difficult to read. When you copy your problem in, and for the blank spaces where latex goes, please just type in the letter/character.
Simplify the following:
sqrt(sqrt(56) sqrt(126))
sqrt(126) = sqrt(9×14) = sqrt(3^2×14):
sqrt(sqrt(56) sqrt(3^2 14))
sqrt(3^2 14) = sqrt(3^2) sqrt(14) = 3^(2/2) sqrt(14) = 3 sqrt(14):
sqrt(sqrt(56)×3 sqrt(14))
sqrt(56) = sqrt(8×7) = sqrt(2^3×7):
sqrt(sqrt(2^3 7) 3 sqrt(14))
sqrt(2^3 7) = sqrt(2^3) sqrt(7) = 2 sqrt(2) sqrt(7):
sqrt(2 sqrt(2) sqrt(7)×3 sqrt(14))
sqrt(2) sqrt(7) = sqrt(2×7):
sqrt(2 sqrt(2×7) 3 sqrt(14))
2×7 = 14:
sqrt(2 sqrt(14)×3 sqrt(14))
2 sqrt(14)×3 sqrt(14) = 2×14×3:
sqrt(2×14×3)
2×14 = 28:
sqrt(28×3)
28×3 = 84:
sqrt(84)
sqrt(84) = sqrt(4×21) = sqrt(2^2×21):
sqrt(2^2 21)
sqrt(2^2 21) = sqrt(2^2) sqrt(21) = 2^(2/2) sqrt(21) = 2 sqrt(21):
2 sqrt(21)
