Đáp án:
\(\begin{array}{l}
e)2\sqrt 7 - 5\\
f) - 1\\
g)1\\
h)6
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
e)\left| {\sqrt 7 - 2} \right| - \left| {\sqrt 7 - 3} \right|\\
= \sqrt 7 - 2 - \left( {3 - \sqrt 7 } \right)\\
= \sqrt 7 - 2 - 3 + \sqrt 7 \\
= 2\sqrt 7 - 5\\
f)\sqrt {5 - 2\sqrt 5 .\sqrt 2 + 2} - \sqrt {5 - 2\sqrt 5 .1 + 1} \\
= \sqrt {{{\left( {\sqrt 5 - 2} \right)}^2}} - \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} \\
= \sqrt 5 - 2 - \left( {\sqrt 5 - 1} \right)\\
= \sqrt 5 - 2 - \sqrt 5 + 1\\
= - 1\\
g)\sqrt {25 - 2.5.\sqrt {17} + 17} + \sqrt {17 - 2.4.\sqrt {17} + 16} \\
= \sqrt {{{\left( {5 - \sqrt {17} } \right)}^2}} + \sqrt {{{\left( {\sqrt {17} - 4} \right)}^2}} \\
= 5 - \sqrt {17} + \sqrt {17} - 4 = 1\\
h)\sqrt {9 + 2.3.\sqrt 5 + 5} + \sqrt {{{\left( {\sqrt 5 - 3} \right)}^2}} \\
= \sqrt {{{\left( {3 + \sqrt 5 } \right)}^2}} + \left| {\sqrt 5 - 3} \right|\\
= 3 + \sqrt 5 + 3 - \sqrt 5 = 6
\end{array}\)
