Question

Tính

a)\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}\)

b)\(\sqrt{75}+\sqrt{48}-\sqrt{300}\)

c)\(\sqrt{3-2\sqrt{2}}+\frac{1}{\sqrt{2}-1}\)

Answer 1

a)   = \(\frac{\sqrt{2}.\sqrt{4+\sqrt{15}}}{\sqrt{2}}+\frac{\sqrt{2}.\sqrt{4-\sqrt{15}}}{\sqrt{2}}\)
      = \(\frac{\sqrt{8+2\sqrt{15}}}{\sqrt{2}}+\frac{\sqrt{8-2\sqrt{15}}}{\sqrt{2}}\)
      =  \(\frac{\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}}{\sqrt{2}}+\frac{\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}}{\sqrt{2}}\)
      = \(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{2}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}\)

      =   \(\frac{2\sqrt{5}}{\sqrt{2}}\)
      =   \(\sqrt{10}\)
b) = \(5\sqrt{3}+4\sqrt{3}-10\sqrt{3}\)

    = \(-\sqrt{3}\)
c) = \(\sqrt{\left(\sqrt{2}-\sqrt{1}\right)^2}+\frac{1\left(\sqrt{2}+1\right)}{2-1}\)
    = \(\sqrt{2}-\sqrt{1}+\frac{1\left(\sqrt{2}+1\right)}{1}\)
    = \(\sqrt{2}-\sqrt{1}+\sqrt{2}+\sqrt{1}\)
    = \(2\sqrt{2}\)
Chúc bạn học tốt ^^