Question 134

The value of $$\sqrt{6 - \sqrt{17 - 2\sqrt{72}}}$$ is closest to:

Solution

$$\sqrt{6 -\sqrt{17 - 2\sqrt{72}}}$$

$$\Rightarrow \sqrt{6 -\sqrt{17-2 \sqrt { 2^2\times 3^2 \times 2 }}} $$

$$\Rightarrow \sqrt { 6 - \sqrt{ 17 - 2\times 6 \sqrt{2 }}} $$

$$\Rightarrow \sqrt {6 - \sqrt {17 - 12 \sqrt {2}}}$$

$$\Rightarrow \sqrt {6 - \sqrt {17-12\times 1.41 }}$$

$$\Rightarrow \sqrt {6 - 0.03 } $$

$$\Rightarrow \sqrt {5.97 } $$

$$\Rightarrow 2.44 Ans $$

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