what,is the square-root of root 5+3
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Let the square root be +- a (1 + b √5)
so √5 + 3 = a² [1 + 5 b² + 2√5 b]
Equate rational and irrational parts.
a² (1+ 5 b²) = 3
2 a² b = 1
Simplify: 1/2b + 5b/2 = 3 1 - 6 b + 5 b^2 = 0
b = [ 3 +- 2]/5 = 1/5 or 1 a² = 5/2 or 1/2
a = √5/√2 or 1/√2
Square root = +- (√5 + 1) / √2
so √5 + 3 = a² [1 + 5 b² + 2√5 b]
Equate rational and irrational parts.
a² (1+ 5 b²) = 3
2 a² b = 1
Simplify: 1/2b + 5b/2 = 3 1 - 6 b + 5 b^2 = 0
b = [ 3 +- 2]/5 = 1/5 or 1 a² = 5/2 or 1/2
a = √5/√2 or 1/√2
Square root = +- (√5 + 1) / √2
kvnmurty:
:)
you could start with +- √a + √b as square root.
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