Question 59

The simplest value of $$\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}$$ is

Solution

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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