Question

if n = (2+(5-(6-3√5+(14-6√5)^1/2)^1/2)^1/2)^1/2)^1/2) . simplify n​

Answer 1

Answer:

n = (2+(5-(6-3√5+(14-6√5)^1/2)^1/2)^1/2)^1/2)^1/2)

Simplifying in steps, starting from inner brackets:

(14-6√5)^1/2=(9+5-2*3*√5)^1/2=((3-√5)²)^1/2=3-√5

(6-3√5+3-√5)^1/2=(5-2*2√5+4)^1/2=((√5-2)²)^1/2=√5-2

(5-(√5-2))^1/2=(5-√5+2)^1/2=(7-√5)^1/2

(2+(7-√5)^1/2)^1/2

n=(2+(7-√5)^1/2)^1/2

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