\(\sqrt{33-20\sqrt{10}}+\dfrac{4}{\sqrt{2}}\)
TG
Những câu hỏi liên quan
Rút gọn biểu thức :
\((5\sqrt{\dfrac{1}{5}}+\dfrac{1}{2}\sqrt{20}-\dfrac{5}{4}\sqrt{\dfrac{4}{5}+\sqrt{5}}):2\sqrt{5}\) và \(\dfrac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{1\dfrac{1}{3}}\)
`(5sqrt{1/5}+1/2sqrt{20}-5/4sqrt{4/5}+sqrt{5}):2/5
`=(sqrt5+1/2*2sqrt5-sqrt{5/4}+sqrt5):2/5`
`=(sqrt5+sqrt5+sqrt5-sqrt5/2):2/5`
`=(5/2*sqrt5):2/5`
`=25/4sqrt5`
Đúng 0
Bình luận (0)
`1/3sqrt{48}+3sqrt{75}-sqrt{27}-10sqrt{1 1/3}`
`=1/3*4sqrt3+3*5sqrt3-3sqrt3-10sqrt{4/3}`
`=4/sqrt3+15sqrt3-3sqrt3-20/sqrt3`
`=12sqrt3-16/sqrt3`
Đúng 1
Bình luận (0)
Giải 5 câu sau:
1. \(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\)
2. \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{2}-\sqrt{5}}\)
3. \(\dfrac{\sqrt{20}-3\sqrt{10}}{3-\sqrt{5}}\)
4. \(\dfrac{6-2\sqrt{5}}{3+\sqrt{5}}\)
5. \(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}\)
1) \(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}=9+4\sqrt{5}\)
2) \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{2}-\sqrt{5}}=\dfrac{\sqrt{10}\left(\sqrt{5}-\sqrt{2}\right)}{-\left(\sqrt{5}-\sqrt{2}\right)}=-\sqrt{10}\)
3) \(\dfrac{\sqrt{20}-3\sqrt{10}}{3-\sqrt{5}}=\dfrac{\sqrt{10}\left(\sqrt{5}-3\right)}{-\left(\sqrt{5}-3\right)}=-\sqrt{10}\)
4) \(\dfrac{6-2\sqrt{5}}{3+\sqrt{5}}=\dfrac{\left(6-2\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}=\dfrac{18-6\sqrt{5}-6\sqrt{5}+10}{4}=\dfrac{28-12\sqrt{5}}{4}=7-3\sqrt{5}\)
5)\(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}=\sqrt{5}+2\)
Đúng 2
Bình luận (0)
\(C=\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
\(B=\dfrac{20}{3+\sqrt{5}+\sqrt{2+2\sqrt{5}}}\)
\(C=\dfrac{\sqrt{10}-\sqrt{5}+2\sqrt{2}+\sqrt{5}-\sqrt{10}-1}{2\sqrt{2}+2+2\sqrt{2}-1+2\sqrt{2}+2}\)
\(=\dfrac{2\sqrt{2}-1}{6\sqrt{2}+3}=\dfrac{9-4\sqrt{2}}{21}\)
\(B=\dfrac{40}{6+2\sqrt{5}+\sqrt{4\sqrt{5}+4}}\)
\(=\dfrac{40}{\left(\sqrt{5}+1\right)^2+2\sqrt{\sqrt{5}+1}}\)
\(=\dfrac{40}{\sqrt{\sqrt{5}+1}\left(\sqrt{\sqrt{5}+1}+2\right)}\)
\(=\dfrac{40\sqrt{\sqrt{5}-1}}{2\left(\sqrt{\sqrt{5}+1}+2\right)}\)
\(=\dfrac{20\left(\sqrt{\sqrt{5}-1}\right)\left(\sqrt{\sqrt{5}+1}-2\right)}{\sqrt{5}+1-4}\)
\(=\dfrac{20\left(\sqrt{\sqrt{5}-1}\right)\left(\sqrt{\sqrt{5}+1}-2\right)}{-3+\sqrt{5}}\)
\(=-5\left(3+\sqrt{5}\right)\left(\sqrt{\sqrt{5}-1}\right)\left(\sqrt{\sqrt{5}+1}-2\right)\)
Đúng 0
Bình luận (0)
1. dfrac{-2}{sqrt{3}-1}2. dfrac{5}{1-sqrt{6}}3. dfrac{2+sqrt{5}}{2-sqrt{5}}4. dfrac{1}{5+2sqrt{6}}5. dfrac{sqrt{5}+2}{sqrt{5}-2}6. dfrac{5sqrt{2}-2sqrt{5}}{sqrt{2}-sqrt{5}}7. dfrac{sqrt{20}-3sqrt{10}}{3-sqrt{2}}8. dfrac{6-2sqrt{5}}{3+sqrt{5}}9. dfrac{9+4sqrt{5}}{sqrt{5}+2}
Đọc tiếp
1. \(\dfrac{-2}{\sqrt{3}-1}\)
2. \(\dfrac{5}{1-\sqrt{6}}\)
3. \(\dfrac{2+\sqrt{5}}{2-\sqrt{5}}\)
4. \(\dfrac{1}{5+2\sqrt{6}}\)
5. \(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\)
6. \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{2}-\sqrt{5}}\)
7. \(\dfrac{\sqrt{20}-3\sqrt{10}}{3-\sqrt{2}}\)
8. \(\dfrac{6-2\sqrt{5}}{3+\sqrt{5}}\)
9. \(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}\)
\(1+\left(\dfrac{2x+\sqrt{x}-1}{1-x}-\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1-x\sqrt{x}}\right):\dfrac{x-\sqrt{x}}{2\sqrt{x}-1}\)
1 ) Rút gọn
2) Tìm x để P=3
3) Tính P tại x 13-\(4\sqrt{10}\)
Bài 1: Rút gọn biểu thức:a) left(5sqrt{dfrac{1}{5}}+dfrac{1}{2}+sqrt{20}-dfrac{5}{4}sqrt{dfrac{4}{5}+sqrt{5}}right)b) dfrac{1}{3}sqrt{48}+3sqrt{75}-sqrt{27}-10sqrt{1dfrac{1}{3}}c) dfrac{5sqrt{7}-7sqrt{5}+2sqrt{70}}{sqrt{35}}d) sqrt{dfrac{3}{4}}+sqrt{dfrac{1}{3}}+sqrt{dfrac{1}{12}}Bài 2: Giải các phương trình sau:a) x^2+4x+52sqrt{2x+3}b) x^2+9x+202sqrt{3x+10}c) x^2+7x+142sqrt{x+4}d) 4sqrt{x+1}x^2-5x+14e) sqrt{6-x}3x-4f) sqrt{5x-9}9-2xMọi người làm ơn giúp mình với. Mình đang cần gấp ạ. Cảm ơn mọi...
Đọc tiếp
Bài 1: Rút gọn biểu thức:
a) \(\left(5\sqrt{\dfrac{1}{5}}+\dfrac{1}{2}+\sqrt{20}-\dfrac{5}{4}\sqrt{\dfrac{4}{5}+\sqrt{5}}\right)\)
b) \(\dfrac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{1\dfrac{1}{3}}\)
c) \(\dfrac{5\sqrt{7}-7\sqrt{5}+2\sqrt{70}}{\sqrt{35}}\)
d) \(\sqrt{\dfrac{3}{4}}+\sqrt{\dfrac{1}{3}}+\sqrt{\dfrac{1}{12}}\)
Bài 2: Giải các phương trình sau:
a) \(x^2+4x+5=2\sqrt{2x+3}\)
b) \(x^2+9x+20=2\sqrt{3x+10}\)
c) \(x^2+7x+14=2\sqrt{x+4}\)
d) \(4\sqrt{x+1}=x^2-5x+14\)
e) \(\sqrt{6-x}=3x-4\)
f) \(\sqrt{5x-9}=9-2x\)
Mọi người làm ơn giúp mình với. Mình đang cần gấp ạ. Cảm ơn mọi người rất nhiều
Bài 1:
a) Ta có: \(\left(5\sqrt{\dfrac{1}{5}}+\dfrac{1}{2}\sqrt{20}-\dfrac{5}{4}\sqrt{\dfrac{4}{5}}+\sqrt{5}\right)\)
\(=\left(\sqrt{5}+\sqrt{5}-\dfrac{5}{4}\cdot\dfrac{2}{\sqrt{5}}+\sqrt{5}\right)\)
\(=3\sqrt{5}-\dfrac{1}{2}\sqrt{5}\)
\(=\dfrac{5}{2}\sqrt{5}\)
c) Ta có: \(\dfrac{5\sqrt{7}-7\sqrt{5}+2\sqrt{70}}{\sqrt{35}}\)
\(=\dfrac{\sqrt{35}\left(\sqrt{5}-\sqrt{7}+2\sqrt{2}\right)}{\sqrt{35}}\)
\(=2\sqrt{2}+\sqrt{5}-\sqrt{7}\)
Đúng 2
Bình luận (0)
Bài 2:
e) ĐKXĐ: \(\dfrac{4}{3}\le x\le6\)
Ta có: \(\sqrt{6-x}=3x-4\)
\(\Leftrightarrow6-x=\left(3x-4\right)^2\)
\(\Leftrightarrow9x^2-24x+16+6-x=0\)
\(\Leftrightarrow9x^2-25x+22=0\)
\(\Delta=\left(-25\right)^2-4\cdot9\cdot22=625-792< 0\)
Vậy: Phương trình vô nghiệm
Đúng 1
Bình luận (0)
Thực hiện phép tính rút gọn sau:
\(A=\sqrt{8}-2\sqrt{18}+3\sqrt{50}\)
\(B=\sqrt{125}-10\sqrt{\dfrac{1}{20}}-\dfrac{\sqrt{5}-5}{\sqrt{5}}\)
\(C=\dfrac{1}{\sqrt{3}+\sqrt{2}}+\sqrt{7-4\sqrt{3}}+\sqrt{2}\)
a: Ta có: \(A=\sqrt{8}-2\sqrt{18}+3\sqrt{50}\)
\(=2\sqrt{2}-6\sqrt{2}+15\sqrt{2}\)
\(=11\sqrt{2}\)
b: Ta có: \(B=\sqrt{125}-10\sqrt{\dfrac{1}{20}}+\dfrac{5-\sqrt{5}}{\sqrt{5}}\)
\(=5\sqrt{5}-\sqrt{5}+\sqrt{5}-1\)
\(=5\sqrt{5}-1\)
Đúng 1
Bình luận (0)
Rút gọn
a) 2sqrt{5}-sqrt{125}-sqrt{80}+sqrt{605}
b) dfrac{10+2sqrt{10}}{sqrt{5}+sqrt{2}}+dfrac{8}{1-sqrt{5}}
c) sqrt{15-sqrt{216}}+sqrt{33-12sqrt{6}}
d) dfrac{2sqrt{8}-sqrt{12}}{sqrt{18}-sqrt{48}}-dfrac{sqrt{5}+sqrt{27}}{sqrt{30}+sqrt{162}}
e) 2sqrt{dfrac{16}{3}}-3sqrt{dfrac{1}{27}}-6sqrt{dfrac{4}{75}}
Đọc tiếp
Rút gọn
a) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
b) \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)
c) \(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
d) \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
e) \(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
a: \(=2\sqrt{5}-5\sqrt{5}-4\sqrt{5}+11\sqrt{5}=4\sqrt{5}\)
b: \(=2\sqrt{5}-2-2\sqrt{5}=-2\)
c: \(=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)
d: \(=\dfrac{2\left(2\sqrt{2}-\sqrt{3}\right)}{\sqrt{6}\left(\sqrt{3}-2\sqrt{2}\right)}-\dfrac{1}{\sqrt{6}}\)
\(=\dfrac{-3}{\sqrt{6}}=-\dfrac{3\sqrt{6}}{6}=-\dfrac{\sqrt{6}}{2}\)
e: \(=\dfrac{8}{3}\sqrt{3}-\dfrac{1}{3}\sqrt{3}-\dfrac{4}{5}\sqrt{3}=\dfrac{23}{15}\sqrt{3}\)
Đúng 0
Bình luận (0)
tính
A=\(\left(1-\sqrt{7}\right).\dfrac{\sqrt{7}+7}{2\sqrt{7}}\)
B=\(3\sqrt{3}+4\sqrt{12}-5\sqrt{27}\)
C=\(\sqrt{32}-\sqrt{50}+\sqrt{18}\)
D=\(\sqrt{72}+\sqrt{4\dfrac{1}{2}}-\sqrt{32}-\sqrt{162}\)
E=\(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)
a: \(A=\left(1-\sqrt{7}\right)\cdot\left(1+\sqrt{7}\right)=1-7=-6\)
b: \(B=3\sqrt{3}+8\sqrt{3}-15\sqrt{3}=-4\sqrt{3}\)
c: \(C=4\sqrt{2}-5\sqrt{2}+3\sqrt{2}=2\sqrt{2}\)
Đúng 1
Bình luận (0)