a.\(\sqrt{5^2}-4^2\)
=\(\sqrt{25-16}\)
=\(\sqrt{9}\)
=\(\sqrt{3^2}\)
=3
b.\(\sqrt{26^2}-24^2\)
=\(\sqrt{676-576}\)
=\(\sqrt{100}\)
=\(\sqrt{10^2}\)
=10
c.\(\sqrt{85^2-84^2}\)
=\(\sqrt{7225-7056}\)
=\(\sqrt{169}\)
=\(\sqrt{13^2}\)
=13
Bài 4:
a: \(\left(\sqrt{\dfrac{2}{3}}+\sqrt{\dfrac{50}{3}}-\sqrt{24}\right)\cdot\sqrt{6}\)
\(=\left(\dfrac{\sqrt{6}}{3}+\dfrac{5\sqrt{2}}{\sqrt{3}}-2\sqrt{6}\right)\cdot\sqrt{6}\)
\(=\left(\dfrac{\sqrt{6}}{3}+\dfrac{5\sqrt{6}}{3}-2\sqrt{6}\right)\cdot\sqrt{6}\)
\(=\sqrt{6}\cdot\sqrt{6}\left(\dfrac{1}{3}+\dfrac{5}{3}-2\right)\)
=0
b: \(\sqrt{3+\sqrt{5}}\cdot\sqrt{2}=\sqrt{6+2\sqrt{5}}\)
\(=\sqrt{5+2\cdot\sqrt{5}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{5}+1\right)^2}=\sqrt{5}+1\)
c: \(\left(\sqrt{\dfrac{3}{4}}-\sqrt{3}+5\cdot\sqrt{\dfrac{4}{3}}\right)\cdot\sqrt{12}\)
\(=\left(\dfrac{1}{2}\sqrt{3}-\sqrt{3}+5\cdot\dfrac{2}{\sqrt{3}}\right)\cdot2\sqrt{3}\)
\(=\left(-\dfrac{1}{2}\sqrt{3}+\dfrac{10}{\sqrt{3}}\right)\cdot2\sqrt{3}\)
\(=-\dfrac{1}{2}\sqrt{3}\cdot2\sqrt{3}+\dfrac{10}{\sqrt{3}}\cdot2\sqrt{3}\)
=-1+20
=19
d: \(\sqrt{3-\sqrt{5}}\cdot\sqrt{8}\)
\(=\sqrt{3-\sqrt{5}}\cdot\sqrt{2}\cdot\sqrt{4}\)
\(=2\cdot\sqrt{6-2\sqrt{5}}=2\left(\sqrt{5}-1\right)=2\sqrt{5}-2\)
