Question

Answer 1

a) \(\sqrt{\left(-9\right)^2}=\left|-9\right|=9\)

b) \(\sqrt{\left(2-\sqrt{5}\right)^2}=\left|2-\sqrt{5}\right|=\sqrt{5}-2\)

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

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

d) \(\sqrt{4+2\sqrt{3}}-\sqrt{3}=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{3}\)

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

e) \(\sqrt{81x^2}+8x\left(x< 0\right)=-9x+8x=-x\)