Question

ae giúp bài 1 vs 2

Answer 1

Bài 1:

a: \(-0,8\cdot\sqrt{\left(-0,125\right)^2}=-0,8\cdot0,125=-0,1\)

b: \(\sqrt{\left(-2\right)^6}=\sqrt{2^6}=\sqrt{8^2}=8\)

c: \(\sqrt{\left(\sqrt3-2\right)^2}=\left|\sqrt3-2\right|=2-\sqrt3\)

d: \(\sqrt{\left(2\sqrt2-3\right)^2}=\left|2\sqrt2-3\right|=3-2\sqrt2\)

e: \(\sqrt{\left(\frac{1}{\sqrt2}-\frac12\right)^2}=\sqrt{\left(\frac{\sqrt2-1}{2}\right)^2}=\left|\frac{\sqrt2-1}{2}\right|=\frac{\sqrt2-1}{2}\)

f: \(\sqrt{\left(0,1-\sqrt{0,1}\right)^2}=\sqrt{\left(\frac{1}{10}-\frac{1}{\sqrt{10}}\right)^2}=\sqrt{\left(\frac{1-\sqrt{10}}{10}\right)^2}=\frac{\sqrt{10}-1}{10}\)

Bài 2:

a: \(\sqrt{\left(3-2\sqrt2\right)^2}+\sqrt{\left(3+2\sqrt2\right)^2}\)

\(=3-2\sqrt2+3+2\sqrt2\)

=3+3

=6

b: \(\sqrt{\left(5-2\sqrt6\right)^2}-\sqrt{\left(5+2\sqrt6\right)^2}\)

\(=\left|5-2\sqrt6\right|-\left|5+2\sqrt6\right|\)

\(=5-2\sqrt6-5-2\sqrt6=-4\sqrt6\)

c: \(\sqrt{\left(2-\sqrt3\right)^2}+\sqrt{\left(1-\sqrt3\right)^2}\)

\(=\left|2-\sqrt3\right|+\left|1-\sqrt3\right|\)

\(=2-\sqrt3+\sqrt3-1=2-1=1\)

d: \(\sqrt{\left(3+\sqrt2\right)^2}-\sqrt{\left(1-\sqrt2\right)^2}\)

\(=3+\sqrt2-\left(\sqrt2-1\right)\)

\(=3+\sqrt2-\sqrt2+1=4\)

e: \(\sqrt{\left(\sqrt5-\sqrt2\right)^2}+\sqrt{\left(\sqrt5+\sqrt2\right)^2}\)

\(=\sqrt5-\sqrt2+\sqrt5+\sqrt2=2\sqrt5\)

f: \(\sqrt{\left(\sqrt2+1\right)^2}-\sqrt{\left(\sqrt2-5\right)^2}\)

\(=\sqrt2+1-\left(5-\sqrt2\right)=\sqrt2+1-5+\sqrt2=-4+2\sqrt2\)