a: \(=\left(0.2-1.2+11\right)\cdot9=12\cdot9=108\)
b: \(=\dfrac{75}{\sqrt{9+16}}-3\cdot4\)
\(=\dfrac{75}{5}-12=15-12=3\)
c: \(=4-\sqrt{15}+\sqrt{15}=4\)
d: \(=2-\sqrt{3}+\sqrt{3}-1=2-1=1\)
e: \(=\sqrt{45-2\cdot3\sqrt{5}\cdot2+4}-\sqrt{45+2\cdot3\sqrt{5}\cdot2+4}\)
\(=3\sqrt{5}-2-3\sqrt{5}-2\)
=-4
f: \(=\sqrt{20+2\cdot2\sqrt{5}\cdot3+9}-\sqrt{20-2\cdot2\sqrt{5}\cdot3+9}\)
\(=2\sqrt{5}+3-2\sqrt{5}+3\)
=6
c) \(\sqrt[]{\left(4-\sqrt[]{15}\right)^2}+\sqrt[]{15}\)
\(=\left|4-\sqrt[]{15}\right|+\sqrt[]{15}\)
\(=4-\sqrt[]{15}+\sqrt[]{15}\left(4>\sqrt[]{15}\right)\)
\(=4\)
d) \(\sqrt[]{\left(2-\sqrt[]{3}\right)^2}+\sqrt[]{\left(1-\sqrt[]{3}\right)^2}\)
\(=\left|2-\sqrt[]{3}\right|+\left|1-\sqrt[]{3}\right|\)
\(=2-\sqrt[]{3}+\sqrt[]{3}-1\left(2>\sqrt[]{3};\sqrt[]{3}>1\right)\)
\(=1\)
e) \(\sqrt[]{49-12\sqrt[]{5}}-\sqrt[]{49+12\sqrt[]{5}}\)
\(=\sqrt[]{45-2.2.3\sqrt[]{5}+4}-\sqrt[]{45+2.2.3\sqrt[]{5}+4}\)
\(=\sqrt[]{\left(3\sqrt[]{5}-2\right)^2}-\sqrt[]{\left(3\sqrt[]{5}+2\right)^2}\)
\(=\left|3\sqrt[]{5}-2\right|-\left|3\sqrt[]{5}+2\right|\)
\(=3\sqrt[]{5}-2-3\sqrt[]{5}-2\left(3\sqrt[]{5}>2\right)\)
\(=-4\)
f) \(\sqrt[]{29+12\sqrt[]{5}}-\sqrt[]{29-12\sqrt[]{5}}\)
\(=\sqrt[]{20+2.3.2\sqrt[]{5}+9}-\sqrt[]{20-2.3.2\sqrt[]{5}+9}\)
\(=\sqrt[]{\left(2\sqrt[]{5}+3\right)^2}-\sqrt[]{\left(2\sqrt[]{5}-3\right)^2}\)
\(=\left|2\sqrt[]{5}+3\right|-\left|2\sqrt[]{5}-3\right|\)
\(=2\sqrt[]{5}+3-2\sqrt[]{5}+3\left(2\sqrt[]{5}>3\right)\)
\(=0\)
a) \(\left(\sqrt[]{0,04}-\sqrt[]{\left(-1,2\right)^2}+\sqrt[]{121}\right).\sqrt[]{81}\)
\(=\left(\sqrt[]{0,2^2}-\sqrt[]{1,2^2}+\sqrt[]{11^2}\right).\sqrt[]{9^2}\)
\(=\left(\left|0,2\right|-\left|1,2\right|+\left|11\right|\right).\left|9\right|\)
\(=\left(0,2-1,2+11\right).9=10.9=90\)
