\(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{9}+2\sqrt{21}\)

=\(\left(\sqrt{4}\sqrt{7}-\sqrt{7}-\sqrt{12}\right).3+2\sqrt{21}\)

=\(\left(2\sqrt{7}-\sqrt{7}-\sqrt{4}\sqrt{3}\right).3+2\sqrt{21}\)

=\(\left(\sqrt{7}-2\sqrt{3}\right).3+2\sqrt{21}\)

=\(3\sqrt{7}-6\sqrt{3}+2\sqrt{21}\)

đề có sai ko nhưng kết quả ra thế

\(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{9}+2\sqrt{21}=\left(2\sqrt{7}-2\sqrt{3}-\sqrt{7}\right).3+2\sqrt{21}=\left(\sqrt{7}-2\sqrt{3}\right).3+2\sqrt{21}=3\sqrt{7}-6\sqrt{3}+2\sqrt{21}\)

Rút gọn

A, \(\dfrac{125}{1000}\)

\(\dfrac{125}{1000}=\dfrac{125:125}{1000:125}=\dfrac{1}{8}\)

B, \(\dfrac{3600-75}{4800-175}\)

\(\dfrac{3600-75}{4800-175}=\dfrac{3525}{4625}\)

\(\Rightarrow\dfrac{3525}{4625}=\dfrac{3525:25}{4625:25}=\dfrac{141}{185}\)

C, \(\dfrac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}\)

\(\dfrac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\dfrac{3^{10}.\left(-5\right)^{20}.\left(-5\right)}{\left(-5\right)^{20}.3^{10}.3^2}=\dfrac{\left(-5\right)}{3^2}=\dfrac{-5}{9}\)

a. = 12 - 25 + 36 - 12 + 36 - 57

= (12 - 12) + (36 + 36) - (25 + 57)

= 0 + 72 - 82

= -10

b. = -23 - 5 + 6 - 17 + 23 - 5 - 83 - 6

= (-23 + 23) + (-5 - 5) + (6 - 6) - (17 + 83)

= 0 + (-10) + 0 - 100

= -110

c.?

a) \(\sqrt{15+2\sqrt{5}-\sqrt{21-4\sqrt{5}}}\)

\(=\sqrt{15+2\sqrt{5}-\sqrt{\left(1-2\sqrt{5}\right)^2}}\)

\(=\sqrt{15+2\sqrt{5}-\left(2\sqrt{5}-1\right)}\)

\(=\sqrt{15+2\sqrt{5}-\left(2\sqrt{5}-1\right)}\)

\(=\sqrt{15+2\sqrt{5}-2\sqrt{5}+1}\)

\(=\sqrt{16}\)

\(=4\)

b) \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

\(=\sqrt[4]{5-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

\(=\sqrt[4]{5-\sqrt{3-\sqrt{\left(3-2\sqrt{5}\right)^2}}}\)

\(=\sqrt[4]{5-\sqrt{3-\left(2\sqrt{5}-3\right)}}\)

\(=\sqrt[4]{5-\sqrt{3-2\sqrt{5}+3}}\)

\(=\sqrt[4]{5-\sqrt{6-2\sqrt{5}}}\)

\(=\sqrt[4]{5-\sqrt{\left(1-\sqrt{5}\right)^2}}\)

\(=\sqrt[4]{5-\left(\sqrt{5}-1\right)}\)

\(=\sqrt[4]{5-\sqrt{5}+1}\)

\(=\sqrt[4]{6-\sqrt{5}}\)

\(\left(\sqrt{5}-\sqrt{7}\right)^2\)=\(\sqrt{5^2}-\sqrt{7^2}\)=\(5-7=-2\)

\(\frac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)=\(\frac{\sqrt{2}\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{7}\left(\sqrt{3}+\sqrt{5}\right)}\)=\(\frac{\sqrt{2}}{\sqrt{7}}\)