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$${\sqrt {a + b} } = {\sqrt a } + {\sqrt b }$$
$${\sqrt {a – b} } = {\sqrt a } – {\sqrt b }$$
$${\sqrt {ab} } = {\sqrt a } {\sqrt b }$$
$${\sqrt {\frac{a}{b}} } = \frac{{\sqrt a }}{{\sqrt b }}$$
$${\sqrt {{a^2}} } = |a|$$
$${\sqrt {{a^2} b} } = |a|{\sqrt b }$$
$${\sqrt[{n}]{a}} = \left| a \right|^{\frac{1}{n}}$$
$${\left( {\sqrt a } \right)^n } = {a^{\frac{n}{2}}}$$
$${\sqrt a + \sqrt b } \times ({\sqrt a – \sqrt b }) = a – b$$
$${a^2} – {b^2} = \left( {a + b} \right)\left( {a – b} \right)$$
$${a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} – ab + {b^2}} \right)$$
$${a^3} – {b^3} = \left( {a – b} \right)\left( {{a^2} + ab + {b^2}} \right)$$
$${x^2} + 2xy + {y^2} = {\left( {x + y} \right)^2}$$
$${x^2} – 2xy + {y^2} = {\left( {x – y} \right)^2}$$
$${\left( {x + y} \right)^3} = {x^3} + 3{x^2}y + 3x{y^2} + {y^3}$$
$${\left( {x – y} \right)^3} = {x^3} – 3{x^2}y + 3x{y^2} – {y^3}$$