a) \(\sqrt{117^2-108^2}=\sqrt{\left(117-108\right)\left(117+108\right)}=\sqrt{9\cdot225}=\sqrt{3^2\cdot15^2}=\left|3\cdot15\right|=45\)
b) \(\sqrt{9-4\sqrt{5}}+2=\sqrt{5-4\sqrt{5}+4}+2=\sqrt{\left(\sqrt{5}-2\right)^2}+2=\left|\sqrt{5}-2\right|+2=\sqrt{5}\)
\(a,\sqrt{117^2-108^2}\\ =\sqrt{\left(117-108\right)\left(117+108\right)}\\ =\sqrt{9.225}\\ =\sqrt{3^2}.\sqrt{15^2}\\ =3.15\\ =45\)
\(b,\sqrt{9-4\sqrt{5}}+2=\sqrt{5}\)
\(VT=\sqrt{9-4\sqrt{5}}+2\\ =\sqrt{\sqrt{5^2}-2.2\sqrt{5}+2^2}+2\\ =\sqrt{\left(\sqrt{5}-2\right)^2}+2\\ =\left|\sqrt{5}-2\right|+2\\ =\sqrt{5}-2+2\\ =\sqrt{5}=VP\left(dpcm\right)\)
a) \(\sqrt{117^2-108^2}\)
\(=\sqrt{\left(117-108\right)\left(117+108\right)}\)
\(=\sqrt{9\cdot225}\)
\(=\sqrt{3^2\cdot15^2}\)
\(=\sqrt{\left(3\cdot15\right)^2}\)
\(=3\cdot15\)
\(=45\)
b) VT: \(\sqrt{9-4\sqrt{5}}+2\)
\(=\sqrt{4-4\sqrt{5}+5}+2\)
\(=\sqrt{2^2-2\cdot2\cdot\sqrt{5}\cdot\left(\sqrt{5}\right)^2}+2\)
\(=\sqrt{\left(2-\sqrt{5}\right)^2}=\left|2-\sqrt{5}\right|+2\)
\(=\sqrt{5}-2+2=\sqrt{5}=VP\) (đpcm)
