The simplest value of $$\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}$$ is
Expression : $$\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}$$
= $$(3\sqrt{2^2\times2}-2\sqrt{2^2\times3}+\sqrt{2^2\times5})\div(3\sqrt{3^2\times2}-2\sqrt{3^2\times3}+\sqrt{3^2\times5})$$
= $$(6\sqrt2-4\sqrt3+2\sqrt5)\div(9\sqrt2-6\sqrt3+3\sqrt5)$$
= $$\frac{2(3\sqrt2-2\sqrt3+\sqrt5)}{3(3\sqrt2-2\sqrt3+\sqrt5)}$$
= $$\frac{2}{3}$$
=> Ans - (B)
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