a) \[\sqrt {x + 1 + 2\sqrt x } \](điều kiện : x ≥ 0)

= \[\sqrt {{{\left( {\sqrt x + 1} \right)}^2}} \]

= \[\left| {\sqrt x + 1} \right|\]

= \[\sqrt x + 1\]

b) \(\sqrt {x - 2 + 2\sqrt {x - 3} } \)(điều kiện: x ≥ 3)

= \(\sqrt {x - 3 + 2\sqrt {x - 3} + 1} \)

= \(\sqrt {{{\left( {\sqrt {x - 3} - 1} \right)}^2}} \)

= \[\left| {\sqrt {x - 3} + 1} \right|\]

= \[\sqrt {x - 3} + 1\]

c) \(\sqrt {2x - 1 - 2\sqrt {2\left( {x - 1} \right)} } \)(điều kiện: x ≥ 1)

= \(\sqrt {2x - 2 - 2\sqrt {2\left( {x - 1} \right)} + 1} \)

= \(\sqrt {2\left( {x - 1} \right) - 2\sqrt {2\left( {x - 1} \right)} + 1} \)

= \(\sqrt {{{\left( {\sqrt {2\left( {x - 1} \right)} - 1} \right)}^2}} \)

= \(\left| {\sqrt {2\left( {x - 1} \right)} - 1} \right|\)

= \(\left| {\sqrt {2\left( {x - 1} \right)} - 1} \right|\).

d) \(\sqrt {2x + 1 + 2\sqrt {2x} } \)(điều kiện: x ≥ 0)

= \(\sqrt {{{\left( {\sqrt {2x} + 1} \right)}^2}} \)

= \(\sqrt {2x} + 1\).