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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}.$

Similar Questions

If $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}=a+b \sqrt{35},$ find the value of $a$ and $b$.

Classify the following numbers as rational or irrational with justification:
$(i)$ $10.124124 \ldots$
$(ii)$ $1.010010001 \ldots$

Find the value of $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$

Express $3.\overline{5}$ in the $\frac{p}{q}$ form.

State whether the following statement is true or false:
Every whole number is a natural number.

Vedclass Test Series

Exam Paper Generator

Online Exam Module