Question

Thực hiện phép tính

a)-0,8.(\(\sqrt{\left(-0,125^{ }\right)}^2\)

b)\(\sqrt{\left(0,1-\sqrt{0,1}\right)^{ }}^2\)

c)\(\sqrt{\left(3-2\sqrt{2}\right)}^2\)+\(\sqrt{\left(3+2\sqrt{2}\right)}^2\)

d)\(\sqrt{\left(\sqrt{2}+1\right)}^2\)-\(\sqrt{\left(\sqrt{2}-5\right)}^2\)

Answer 1

a: \(=-0.8\cdot0.125=-0.1\)

b: \(=0.1-\sqrt{0.1}\)

c: \(=3-2\sqrt{2}+3+2\sqrt{2}=6\)

d: \(=\sqrt{2}+1-\left(5-\sqrt{2}\right)=2\sqrt{2}-4\)

Answer 2

`a)`\(-0,8.\sqrt{\left(-0,125\right)^2}=-0,8.0,125=-0,1\)

`b)`\(\sqrt{\left(0,1-\sqrt{0,1}\right)^2}=\left|0,1-\sqrt{0,1}\right|=0,1-\sqrt{0,1}\)

`c)`\(\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(3+2\sqrt{2}\right)^2}=\left|3-\sqrt{2}\right|+\left|3+\sqrt{2}\right|=3-\sqrt{2}+3+\sqrt{2}=6\)

`d)`\(\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}=\left|\sqrt{2}+1\right|-\left|\sqrt{2}-5\right|=\sqrt{2}+1-\left(5-\sqrt{2}\right)=\sqrt{2}+1-5+\sqrt{2}=2\sqrt{2}-4\)

Answer 3

\(a,-0,8.\sqrt{\left(-0,125\right)^2}=-0,8.\left|-0,125\right|=-0,8.0,125=-0,1\)

\(c,\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(3+2\sqrt{2}\right)^2}=\left|3-2\sqrt{2}\right|+\left|3+2\sqrt{2}\right|=3-2\sqrt{2}+3+2\sqrt{2}=6\)

\(b,\sqrt{\left(0,1-\sqrt{0,1}\right)^2}=\left|0,1-\sqrt{0,1}\right|=0,1-\sqrt{0,1}\)

\(d,\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}=\left|\sqrt{2}+1\right|-\left|\sqrt{2}-5\right|=\sqrt{2}+1-5+\sqrt{2}=2\sqrt{2}-4\)