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$\sqrt{ 1.5 ^ { \color{#FF6800}{ 2 } } } - \left ( - \sqrt{ 3 } \right ) ^ { 2 } \div \sqrt{ \left ( - 2 \right ) ^ { 2 } }$

$ $ Organize as the power is written in the radical sign, and the root exponent and the exponent are the same $ $

$\color{#FF6800}{ 1.5 } - \left ( - \sqrt{ 3 } \right ) ^ { 2 } \div \sqrt{ \left ( - 2 \right ) ^ { 2 } }$

$\color{#FF6800}{ 1.5 } - \left ( - \sqrt{ 3 } \right ) ^ { 2 } \div \sqrt{ \left ( - 2 \right ) ^ { 2 } }$

$ $ Convert decimals to fractions $ $

$\color{#FF6800}{ \dfrac { 3 } { 2 } } - \left ( - \sqrt{ 3 } \right ) ^ { 2 } \div \sqrt{ \left ( - 2 \right ) ^ { 2 } }$

$\dfrac { 3 } { 2 } - \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \div \sqrt{ \left ( - 2 \right ) ^ { 2 } }$

$ $ Remove negative signs because negative numbers raised to even powers are positive $ $

$\dfrac { 3 } { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } \div \sqrt{ \left ( - 2 \right ) ^ { 2 } }$

$\dfrac { 3 } { 2 } - \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \div \sqrt{ \left ( - 2 \right ) ^ { 2 } }$

$ $ If you square the radical sign, it will disappear $ $

$\dfrac { 3 } { 2 } - \color{#FF6800}{ 3 } \div \sqrt{ \left ( - 2 \right ) ^ { 2 } }$

$\dfrac { 3 } { 2 } - 3 \div \sqrt{ \left ( - 2 \right ) ^ { \color{#FF6800}{ 2 } } }$

$ $ Organize as the power is written in the radical sign, and the root exponent and the exponent are the same $ $

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

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

$ $ Divide $ 3 $ by $ 2$

$\dfrac { 3 } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } }$

$\color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } }$

$ $ Remove the two numbers if the values are the same and the signs are different $ $

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