Question

$(3 \sqrt{2} \div \sqrt{6} - \sqrt{3} ) + (2 \sqrt{3} \div \sqrt{6} + 2) - (4 \sqrt{3} \div \sqrt{6} - \sqrt{2} )$
​

Answer 1

Answer : 1.31784

Step by step explanation :

$(3 \sqrt{2} \div \sqrt{6} - 3) + (2 \sqrt{3} \div 6 + 2) - (4 \sqrt{3} \div 6 - 2)$

Write the division as a fraction

$= > ( \frac{3 \sqrt{2} }{ \sqrt{6} } - 3) + ( \frac{2 \sqrt{3} }{ \sqrt{6} } + 2) - ( \frac{4 \sqrt{3} }{ \sqrt{6} } - 2)$

Simplify the expressions

$= > ( \frac{3}{ \sqrt{3} } - 3) + ( \frac{2}{ \sqrt{2} } + 2) - ( \frac{4}{ \sqrt{2} } - 2)$

Remove unnecessary parenthesis.

$= > \frac{3}{ \sqrt{3} } - 3 + ( \frac{2}{ \sqrt{2} } + 2) - ( \frac{4}{ \sqrt{2} } - 2)$

When there is a "+" in front of the parenthesis the expression remains the same.

$= > \frac{3}{ \sqrt{3} } - 3 + \frac{2}{ \sqrt{2} } + 2 - ( \frac{4}{ \sqrt{2} } - 2)$

Rationalize the denominator

$= > \frac{3}{ \sqrt{3} } - 3 + \frac{2}{ \sqrt{2} } + 2 - (2 \sqrt{2} - 2)$

Rationalize the denominators

$= > \sqrt{3} - 3 + \sqrt{2} + 2 - (2 \sqrt{2} - 2)$

When there is a "-" in front of the parenthesis, change the sign of each term in parenthesis.

$= > \sqrt{3} - 3 + \sqrt{2} + 2 - 2 \sqrt{2} + 2$

Calculate the sum or difference.

$= > \sqrt{3} + 1 + \sqrt{2} - 2 \sqrt{2}$

Collect the like terms.

$= > \sqrt{3 } + 1 - \sqrt{2}$

$= > 1.31784$