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: $(2-7\sqrt{5})$
Answer (1)
22nd Jan, 2024
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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