Let (R*,) be the multiplicative group of nonzero real numbers. Show that H = {a+b5 a,b...

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Let (R*,) be the multiplicative group of nonzero real numbers. Show that H = {a+b√5 a,b € Q,a+b√5 + 0} is a subgroup of R* (Helpful along the way: you can use that √5 is not rational, so if a +b√5=0 with a, b E Q, then a = b = 0). Let (R*,) be the multiplicative group of nonzero real numbers. Show that H = {a+b√5 a,b € Q,a+b√5 + 0} is a subgroup of R* (Helpful along the way: you can use that √5 is not rational, so if a +b√5=0 with a, b E Q, then a = b = 0).

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