Question : What is the value of the positive square root of $(69+28\sqrt{5})$?
Option 1: $(7+2\sqrt{5})$
Option 2: $(7-2\sqrt{5})$
Option 3: $(2+7\sqrt{5})$
Option 4: $(2-7\sqrt{5})$
Correct Answer: $(7+2\sqrt{5})$
Solution : Given: $x = 69+28\sqrt{5}$ $⇒ x = 49+20+2×7×2\sqrt{5}$ $⇒ x = 7^2+(2\sqrt{5})^2+2×7×2\sqrt{5}$ $⇒ x = (7+2\sqrt{5})^2$ So, the positive square root of $x$ is $(7+2\sqrt{5})$. Hence, the correct answer is $(7+2\sqrt{5})$.
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