If sqrt{2}=1.414 and sqrt{3}=1.732, find the | vedclass

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Question

(A) Given expression: $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}$Taking the common denominator $(3\sqrt{3}-2\sqrt{2})(3\sqrt{3}+2\sq

Vedclass · Accepted Answer

$2.063$

Vedclass · Answer

(A) Given expression: $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}$Taking the common denominator $(3\sqrt{3}-2\sqrt{2})(3\sqrt{3}+2\sqrt{2})$:$= \frac{4(3\sqrt{3}+2\sqrt{2}) + 3(3\sqrt{3}-2\sqrt{2})}{(3\sqrt{3})^2 - (2\sqrt{2})^2}$$= \frac{12\sqrt{3} + 8\sqrt{2} + 9\sqrt{3} - 6\sqrt{2}}{27 - 8}$$= \frac{21\sqrt{3} + 2\sqrt{2}}{19}$Substituting the values $\sqrt{3}=1.732$ and $\sqrt{2}=1.414$:$= \frac{21(1.732) + 2(1.414)}{19}$$= \frac{36.372 + 2.828}{19}$$= \frac{39.2}{19} \approx 2.063$

If $\sqrt{2}=1.414$ and $\sqrt{3}=1.732,$ find the value of $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}.$

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