Question

Evaluate the expression : 3%2+2%3+√3+√2​

Answer 1

$\huge\color{lime}\ \boxed{\colorbox{black}{Answer : ♞ }}$

$Express \: \frac{3}{100}\times 2 \\ as \: a \: single \: fraction.$

$= > \frac{3\times 2}{100}+\frac{2}{100}\times 3+\sqrt{3}+\sqrt{2}$

$Multiply \: 3 \: and \: 2 \: to \: get \: 6.$

$= > \frac{6}{100}+\frac{2}{100}\times 3+\sqrt{3}+\sqrt{2}$

$Reduce \: the \: fraction \: \frac{6}{100} \: to \: \\ lowest \: terms \: by \: extracting \: and \\ canceling \: out \: 2.$

$= > \frac{3}{50}+\frac{2}{100}\times 3+\sqrt{3}+\sqrt{2}$

$Reduce \: the \: fraction \: \frac{2}{100} \: to \\ lowest \: terms \: by \: extracting \: and \\ canceling \: out \: 2.$

$= > \frac{3}{50}+\frac{1}{50}\times 3+\sqrt{3}+\sqrt{2}$

$Multiply \: \frac{1}{50} \: and \: 3 to \: get \: \frac{3}{50}.$

$= > \frac{3}{50}+\frac{3}{50}+\sqrt{3}+\sqrt{2}$

$Since \: \frac{3}{50} \: and \frac{3}{50} \: have \: the \\ same \: denominator, \: add \: them \: \\ by \: adding \: their \: numerators.$

$= > \frac{3+3}{50}+\sqrt{3}+\sqrt{2}$

$Add \: 3 \: and \: 3 \: to \: get \: 6.$

$= > \frac{6}{50}+\sqrt{3}+\sqrt{2}$

$Reduce \: the \: fraction \: \frac{6}{50} \: to \\ lowest \: terms \: by \: extracting \: and \\ canceling \: out \: 2.$

$= > \frac{3}{25}+\sqrt{3}+\sqrt{2}$

$factor :$

$\: \: \: \: \: \color{blue} \frac{25 \sqrt{2} + 25 \sqrt{3} + 3}{25} \approx 3.26626437$