Question

Answer 1

1)
\(=3-\sqrt{2}\)
2)
\(=1+\sqrt{5}\)
3)
\(=\sqrt{3}-1\)
4)
\(=\left(4-\sqrt{2}\right)^2=16-4\sqrt{2}+2=18-4\sqrt{2}\)
5)
\(=2+\sqrt{5}-\sqrt{5}+2\)
6)
\(=\sqrt{\left(3-\sqrt{5}\right)^2}+\sqrt{5}-1=3-\sqrt{5}+\sqrt{5}-1=2\)
7)
\(\left(3-\sqrt{2}\right).\sqrt{\left(3+\sqrt{2}\right)^2}=\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)=9-2=7\)

Answer 2

1.\(=\left|3-\sqrt{2}\right|=3-\sqrt{2}\)

2.\(=\left|1+\sqrt{5}\right|=1+\sqrt{5}\)

3.\(=\left|1-\sqrt{3}\right|=\sqrt{3}-1\)

4.\(=\left(4-\sqrt{2}\right)^2\)

5.\(=\left|2+\sqrt{5}\right|-\left|2-\sqrt{5}\right|=2+\sqrt{5}-\left(\sqrt{5}-2\right)\)

=\(2+\sqrt{5}-\sqrt{5}+2=4\)

6.\(=\sqrt{\left(3-\sqrt{5}\right)^2}+\left|1-\sqrt{5}\right|=\left|3-\sqrt{5}\right|+\left(\sqrt{5}-1\right)\)

=\(3-\sqrt{5}+\sqrt{5}-1=2\)

7.\(=\left(3-\sqrt{2}\right)\sqrt{\left(3+\sqrt{2}\right)^2}=\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)\)

=9-4=5