Question 102

What is the value of positive square root of $$69+28\sqrt{5}$$ ?

Solution

Let $$x=69+28\sqrt5$$

=> $$x=69+2(2)(7)(\sqrt{5})$$

=> $$x=(49)+(20)+2(7)(2\sqrt5)$$

=> $$x=(7)^2+(2\sqrt5)^2+2(7)(2\sqrt5)$$

=> $$x=(7+2\sqrt5)^2$$

=> Positive square root of $$x=7+2\sqrt5$$

=> Ans - (A)


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