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(C) Given expression: $\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$Rationalize the first term: $\frac{4(3 \sqrt{3}+2 \sqrt{2})}{

Vedclass · Accepted Answer

$2.063$

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(C) Given expression: $\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$Rationalize the first term: $\frac{4(3 \sqrt{3}+2 \sqrt{2})}{(3 \sqrt{3}-2 \sqrt{2})(3 \sqrt{3}+2 \sqrt{2})} = \frac{12 \sqrt{3}+8 \sqrt{2}}{(3 \sqrt{3})^2 - (2 \sqrt{2})^2} = \frac{12 \sqrt{3}+8 \sqrt{2}}{27-8} = \frac{12 \sqrt{3}+8 \sqrt{2}}{19}$Rationalize the second term: $\frac{3(3 \sqrt{3}-2 \sqrt{2})}{(3 \sqrt{3}+2 \sqrt{2})(3 \sqrt{3}-2 \sqrt{2})} = \frac{9 \sqrt{3}-6 \sqrt{2}}{27-8} = \frac{9 \sqrt{3}-6 \sqrt{2}}{19}$Adding both terms: $\frac{12 \sqrt{3}+8 \sqrt{2} + 9 \sqrt{3}-6 \sqrt{2}}{19} = \frac{21 \sqrt{3}+2 \sqrt{2}}{19}$Substitute the values $\sqrt{3} = 1.732$ and $\sqrt{2} = 1.414$:$= \frac{21(1.732) + 2(1.414)}{19} = \frac{36.372 + 2.828}{19} = \frac{39.2}{19} \approx 2.06315...$Rounding to three decimal places,we get $2.063$.

Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Take $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.
$\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$

Similar Questions

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

After rationalizing the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}},$ we get the denominator as

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three decimal places.
$\frac{\sqrt{10}-\sqrt{5}}{2}$

Rationalise the denominator of the following:
$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

Rationalise the denominator in each of the following:
$\frac{18}{3 \sqrt{2}-2 \sqrt{3}}$

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Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Take $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.$\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$