Instructions

What value will come in place of the question mark (?) in the following questions.

Question 129

$$(13+2\sqrt{5})^{2}=?\times\sqrt{5}+189$$

Solution

Expression : $$(13+2\sqrt{5})^{2}=?\times\sqrt{5}+189$$

Using : $$(a + b)^2 = a^2 + b^2 + 2ab$$

=> $$(13)^2 + (2\sqrt{5})^2 + (2.13.2\sqrt{5}) = (x \times \sqrt{5}) + 189$$

=> $$169 + 20 + 52\sqrt{5} = x\sqrt{5} + 189$$

=> $$189 + 52\sqrt{5} = x\sqrt{5} + 189$$

Comparing both sides, we get :

=> $$x = 52$$

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