Question 127

The value of $$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$$ is

Solution

we need to find value of $$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$$

$$\sqrt{7 + \sqrt3}$$ = $$\sqrt{2^2 + (\sqrt3)^2 + 2 \times 2 \times \sqrt3}$$ = $$2 + \sqrt3$$

$$\sqrt{3 + 4^2 + 2 \times 4 \times \sqrt3}$$ = $$4 + \sqrt3$$

$$\sqrt{-\surd3 + 4 + \surd3}$$ = 2\

hence $$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$$ = 2

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