Question 4

The value of $$\sqrt{28+10\sqrt{3}}-\sqrt{7-4\sqrt{3}}$$ is closest to:

Solution

$$\sqrt{28+10\sqrt{3}}-\sqrt{7-4\sqrt{3}}$$
= $$\sqrt{(5)^2 + (\sqrt{3})^2 + 2\times 5 \sqrt{3}}-\sqrt{(2)^2 + (\sqrt{3})^2 - 2 \times 2 \sqrt{3}}$$
= $$\sqrt{(5 + \sqrt{3})^2 } - \sqrt{(2 - \sqrt{3})^2}$$
= $$5 + \sqrt{3} -2 + \sqrt{3}$$
= $$3 + 2\sqrt{3}$$
= 3 + 2$$\times$$ 1.732
= 3 + 3.464
= 6.464 ~ 6.5

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