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$\sqrt{ \color{#FF6800}{ 27 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 2 } { \sqrt{ 6 } } } - \sqrt{ 40 } \div \dfrac { \sqrt{ 5 } } { 2 }$

$ $ Arrange the terms multiplied by fractions $ $

$\color{#FF6800}{ \dfrac { \sqrt{ 27 } \times 2 } { \sqrt{ 6 } } } - \sqrt{ 40 } \div \dfrac { \sqrt{ 5 } } { 2 }$

$\color{#FF6800}{ \dfrac { \sqrt{ 27 } \times 2 } { \sqrt{ 6 } } } - \sqrt{ 40 } \div \dfrac { \sqrt{ 5 } } { 2 }$

$ $ Calculate the expression $ $

$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 40 } \div \dfrac { \sqrt{ 5 } } { 2 }$

$3 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 40 } } \color{#FF6800}{ \div } \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 2 } }$

$ $ Arrange the terms multiplied by fractions $ $

$3 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ 40 } \times 2 } { \sqrt{ 5 } } }$

$3 \sqrt{ 2 } - \color{#FF6800}{ \dfrac { \sqrt{ 40 } \times 2 } { \sqrt{ 5 } } }$

$ $ Calculate the expression $ $

$3 \sqrt{ 2 } - \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right )$

$3 \sqrt{ 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right )$

$ $ Get rid of unnecessary parentheses $ $

$3 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } }$

$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } }$

$ $ Calculate between similar terms $ $

$\color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 2 } }$

$\color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ 2 }$

$ $ Multiplying any number by 1 does not change the value $ $

$- \sqrt{ 2 }$