a) \(75.20,9+5^2.20,9\)

\(=20,9\left(75+5^2\right)\)

\(=20,9\left(75+25\right)\)

\(=20,9.100\)

\(=2090\)

b) \(86.15+150.1,4\)

\(=15\left(86+10.1,4\right)\)

\(=15\left(86+14\right)=15.100=1500\)

c) \(93.32+14.16\)

\(=16\left(93.2+14\right)\)

\(=16\left(186+14\right)=16.200=3200\)

d) \(98,6.199-990.9,86\)

\(=9,86\left(10.199-990\right)=9,86\left(1990-990\right)\)

\(=9,86.1000=9860\)

e) \(-8.40+2.108+24\)

\(=-8.40+2.4.27+8.3\)

\(=-8\left(40-27-3\right)=-8.10=-80\)

a: \(2\sqrt{8\sqrt{3}}-\sqrt{2\sqrt{3}}-\sqrt{9\sqrt{12}}\)

\(=2\sqrt{4\cdot2\sqrt{3}}-\sqrt{2\sqrt{3}}-\sqrt{9\cdot2\sqrt{3}}\)

\(=4\sqrt{2\sqrt{3}}-\sqrt{2\sqrt{3}}-3\sqrt{2\sqrt{3}}\)

=0

b: \(\sqrt{3}+\sqrt{7-4\sqrt{3}}\)

\(=\sqrt{3}+\sqrt{\left(2-\sqrt{3}\right)^2}\)

\(=\sqrt{3}+\left|2-\sqrt{3}\right|\)

\(=\sqrt{3}+2-\sqrt{3}\)

=2

c: \(\sqrt{\left(\sqrt{7}-4\right)^2}-\sqrt{28}+\sqrt{63}\)

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

\(=4-\sqrt{7}+\sqrt{7}\)

=4

d: \(\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):\sqrt{10}\)

\(=\dfrac{\sqrt{10}\left(15\sqrt{5}+5\sqrt{20}-3\sqrt{45}\right)}{\sqrt{10}}\)

\(=15\sqrt{5}+5\sqrt{20}-3\sqrt{45}\)

\(=15\sqrt{5}+5\cdot2\sqrt{5}-3\cdot3\sqrt{5}\)

\(=16\sqrt{5}\)

e: \(\sqrt{3}-2\sqrt{48}+3\sqrt{75}-4\sqrt{108}\)

\(=\sqrt{3}-2\cdot4\sqrt{3}+3\cdot5\sqrt{3}-4\cdot6\sqrt{3}\)

\(=\sqrt{3}-8\sqrt{3}+15\sqrt{3}-24\sqrt{3}\)

\(=-16\sqrt{3}\)

Trần Thị Mai Lan , sau khi học xong về nhà tui ik làm bài tập mà thầy giao cho và đây là bài đó 

a) \(3\sqrt{3}-3\sqrt{4^2\cdot3}+2\sqrt{6^2\cdot3}-\left(2-\sqrt{3}\right)\)

\(3\sqrt{3}-3\cdot4\sqrt{3}+2\cdot6\sqrt{3}-2+\sqrt{3}\)

\(3\sqrt{3}-12\sqrt{3}+12\sqrt{3}-2+\sqrt{3}\)

\(4\sqrt{3}-2\)

b) \(3\sqrt{2}\left(\sqrt{5^2\cdot2}-2\sqrt{3^2\cdot2}+\sqrt{7^2\cdot2}\right)\)

\(3\sqrt{2}\left(5\sqrt{2}-6\sqrt{2}+7\sqrt{2}\right)\)

\(3\sqrt{2}\left(6\sqrt{2}\right)\) \(=36\)

\(a=\sqrt{27}-3\sqrt{48}+2\sqrt{108}-\sqrt{\left(2-\sqrt{3}\right)^2}\)

\(a=3\sqrt{3}-3\sqrt{48}+\sqrt{216}-2+\sqrt{3}\)

\(a=3\sqrt{3}-3\sqrt{48}+3\sqrt{24}-2+\sqrt{3}\)

\(a=3\left(\sqrt{3}-\sqrt{48}+\sqrt{24}+1\right)-2\)

Tính cái trong ngoặc là \(ok\).Em lười đi lấy máy tính lắm

\(b=3\sqrt{2}\left(\sqrt{50}-2\sqrt{18}+\sqrt{98}\right)\)

\(b=3\sqrt{100}-3\sqrt{72}+3\sqrt{196}\)

\(b=3\left(\sqrt{100}-\sqrt{72}+\sqrt{196}\right)\)(Tính trong ngoặc)

a) = 13 x 24 + 24 x 76 + 11 x 24 d)= (1-2-3+4)+(5-6-7+8)+...+(97-98-99+100)

= 24 x ( 13 + 76 + 11 ) = 0 + 0 +...+ 0

= 24 x 100 =0

= 2400

CÓ VIỆC BẬN NÊN MÌNH CHỈ LÀM ĐC ĐẾN ĐÓ THÔI !

d) 1-2-3+4+5-6-7+...+97-98-99+100

=(1-2-3+4)+(5-6-7+8)+(9-10-11+12)+......+(97-98-99+100)

=0+0+0+0+.....+0

=0

Vay bang 0

c) (2+4+6+...+100) . (36.333-108-111)

Ta chia hai tich tren la A va B, ta co:

A=(2+4+6+...+100)

B=(36.333-108-111)

A co ssh la:(100-2):2+1=45(ssh)

B=36.333-108-111

=>

A=(100+2)x45:2=2295

B=36.(111.3)-108-111=111.(36.3)-108-111=111.108-108.1-111=(111.8-108.1)-111=11880-111=11769

=>

A.B =2295.11769=( bam may tinh )27009855

a: \(5\sqrt{2}-8\sqrt{3}+30\sqrt{3}-6\sqrt{3}=5\sqrt{2}+16\sqrt{3}\)

b: \(=14\sqrt{3}-\dfrac{3}{32}\cdot8\sqrt{3}+\dfrac{4}{18}\cdot9\sqrt{3}-\dfrac{1}{10}\cdot10\sqrt{3}\)

\(=14\sqrt{3}-\dfrac{3}{4}\sqrt{3}+2\sqrt{3}-1\sqrt{3}=\dfrac{57}{4}\sqrt{3}\)

c: \(=\dfrac{-1}{2}\cdot6\sqrt{3}+\dfrac{1}{15}\cdot5\sqrt{3}-\dfrac{1}{22}\cdot11\sqrt{3}+2\sqrt{3}\)

\(=-3\sqrt{3}+\dfrac{1}{3}\sqrt{3}-\dfrac{1}{2}\sqrt{3}+2\sqrt{3}=-\dfrac{7}{6}\sqrt{3}\)

d: \(=\dfrac{5}{8}\cdot4\sqrt{3}-\dfrac{1}{33}\cdot11\sqrt{3}+\dfrac{3}{14}\cdot7\sqrt{3}-\dfrac{1}{4}\cdot8\sqrt{3}\)

\(=\dfrac{5}{2}\sqrt{3}-\dfrac{1}{3}\sqrt{3}+\dfrac{3}{2}\sqrt{3}-2\sqrt{3}=\dfrac{5}{3}\sqrt{3}\)

                                                         Bài giải

Ta có :

\(2^{91}=2^{90}\cdot2=\left(2^3\right)^{30}\cdot2=8^{30}\cdot2>5^{30}\)

\(\Rightarrow\text{ }2^{91}>5^{30}\)

\(21^8=\left(21^2\right)^4=441^4>54^4\)

\(\Rightarrow\text{ }54^4< 21^8\)

\(108^{50}=\left(108^2\right)^{25}=11664^{25}\)

\(73^{75}=\left(73^3\right)^{25}=389017^{25}\)

\(\text{Vì }11664^{25}< 389017^{25}\text{ }\Rightarrow\text{ }108^{50}< 73^{75}\)

                                                         Bài giải

\(2^{91}=2^{90}\cdot2=\left(2^3\right)^{30}\cdot2=8^{30}\cdot2>5^{30}\)

\(\Rightarrow\text{ }2^{91}>5^{30}\)

\(21^8=\left(21^2\right)^4=441^4>54^4\)

\(\Rightarrow\text{ }54^4< 21^8\)

\(108^{50}=\left(108^2\right)^{25}=11664^{25}\)

\(73^{75}=\left(73^3\right)^{25}=389017^{25}\)

\(\text{Vì }11664^{25}< 389017^{25}\text{ }\Rightarrow\text{ }108^{50}< 73^{75}\)

\(1,\sqrt{432}-\sqrt{363}+\sqrt{48}-\sqrt{75}+\sqrt{108}-\sqrt{147}\)

\(=\sqrt{12^2.3}-\sqrt{11^2.3}+\sqrt{4^2.3}-\sqrt{5^2.3}+\sqrt{6^2.3}-\sqrt{7^2.3}\)

\(=12\sqrt{3}-11\sqrt{3}+4\sqrt{3}-5\sqrt{3}+6\sqrt{3}-7\sqrt{3}\)

\(=\sqrt{3}.\left(12-11+4-5+6-7\right)\)

\(=-\sqrt{3}\)

\(2,6\sqrt{60}-5\sqrt{8}+3\sqrt{15}+4\sqrt{32}+3\sqrt{128}-2\sqrt{1250}\)

\(=6.2\sqrt{15}-5.2\sqrt{2}+3\sqrt{15}+4.4\sqrt{2}+3.8\sqrt{2}-2.25\sqrt{2}\)

\(=12\sqrt{15}+3\sqrt{15}-10\sqrt{2}+16\sqrt{2}+24\sqrt{2}-50\sqrt{2}\)

\(=\sqrt{15}.\left(12+3\right)+\sqrt{2}.\left(-10+16+24-50\right)\)

\(=15\sqrt{15}-20\sqrt{2}\)

1/ \(\sqrt{432}-\sqrt{363}+\sqrt{48}-\sqrt{75}+\sqrt{108}-\sqrt{147}\)

\(=12\sqrt{3}-11\sqrt{3}+4\sqrt{3}-5\sqrt{3}+6\sqrt{3}-7\sqrt{3}\)

\(=\left(12-11+4-5+6-7\right)\sqrt{3}\)

\(=-\sqrt{3}\)

2/ \(6\sqrt{60}-5\sqrt{8}+3\sqrt{15}+4\sqrt{32}+3\sqrt{128}-2\sqrt{1250}\)

\(=12\sqrt{15}-10\sqrt{2}+3\sqrt{15}+16\sqrt{2}+24\sqrt{2}-50\sqrt{2}\)

\(=\left(12+3\right)\sqrt{15}+\left(-10+16+24-50\right)\sqrt{2}\)

\(=15\sqrt{15}-20\sqrt{2}\)