Question

Answer 1

a; A = \(\sqrt{32.200}\)

    A = \(\sqrt{6400}\)

   A = \(\sqrt{80^2}\)

   A = 80

b;  B = \(\sqrt{5}\).\(\sqrt{125}\)

     B = \(\sqrt{5.125}\)

     B = \(\sqrt{5.5^3}\)

     B = \(\sqrt{5^4}\)

     B = 5²

     B = 25

c; C = \(\sqrt{\left(9+2\sqrt{14}\right)\left(9-2\sqrt{14}\right)}\)

     C = \(\sqrt{81-4.14}\)

     C = \(\sqrt{81-56}\)

     C =  \(\sqrt{25}\)

     C = 5

d; D = \(\sqrt{117,5^2-26,5^2-1440}\)

     D = \(\sqrt{13806,25-702,25-1440}\)

     D  = \(\sqrt{13104-1440}\)

     D = \(\sqrt{11664}\)

     D = 108

Answer 2

\(A=\sqrt{32.200}=\sqrt{4^2.2.10^2.2}=\sqrt{4^2.2^2.10^2}=4.2.10=80\)

\(B=\sqrt{5}.\sqrt{125}=\sqrt{5}.\sqrt{5^3}=\sqrt{5.5^3}=\sqrt{5^4}=5^2=25\)

\(C=\sqrt{\left(9+2\sqrt{14}\right)\left(9-2\sqrt{14}\right)}=\sqrt{9^2-\left(2\sqrt{14}\right)^2}=\sqrt{25}=5\)

\(D=\sqrt{117,5^2-26,5^2-1440}=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-1440}\)

\(=\sqrt{91.144-144.10}=\sqrt{144.\left(91-10\right)}=\sqrt{144.81}\)

\(=\sqrt{12^2.9^2}=12.9=108\)