Tính:
a)\(\sqrt{3\sqrt{2}-2\sqrt{3}}\cdot\sqrt{3\sqrt{2}+2\sqrt{3}}\)
b) \(\sqrt{2+2\sqrt{2-\sqrt{2}}}\cdot\sqrt{2-2\sqrt{2-\sqrt{2}}}\)
c)\(\left(\sqrt{2}-\sqrt{7}\right)\sqrt{9+2\sqrt{14}}\)
Những câu hỏi liên quan
TÍNH :Asqrt{3+sqrt{5+2sqrt{3}}}cdotsqrt{3-sqrt{5+2sqrt{3}}}Bsqrt{4+sqrt{8}}cdotsqrt{2+sqrt{2+sqrt{2}}}cdotsqrt{2-sqrt{2+sqrt{2}}}Csqrt{2+sqrt{3}}cdotsqrt{2+sqrt{2+sqrt{3}}}cdotsqrt{2+sqrt{2+sqrt{2+sqrt{3}}}}cdotsqrt{2-sqrt{2+sqrt{2+sqrt{3}}}}Dleft[4+sqrt{15}right]left[sqrt{10}-sqrt{6}right]cdotsqrt{4-sqrt{15}}Eleft[3-sqrt{5}right]cdotsqrt{3+sqrt{5}}text{ }+left[3+sqrt{5}right]cdotsqrt{3-sqrt{5}}
Đọc tiếp
TÍNH :
\(A=\sqrt{3+\sqrt{5+2\sqrt{3}}}\cdot\sqrt{3-\sqrt{5+2\sqrt{3}}}\)
\(B=\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(C=\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
\(D=\left[4+\sqrt{15}\right]\left[\sqrt{10}-\sqrt{6}\right]\cdot\sqrt{4-\sqrt{15}}\)
\(E=\left[3-\sqrt{5}\right]\cdot\sqrt{3+\sqrt{5}}\text{ }+\left[3+\sqrt{5}\right]\cdot\sqrt{3-\sqrt{5}}\)
\(A=\sqrt{3+\sqrt{5+2\sqrt{3}}.\sqrt{3-\sqrt{5+2\sqrt{3}}}}=\sqrt{\left(3^2\right)-\left(\sqrt{5+2\sqrt{3}}\right)^2}\)
\(=\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\)
\(B=\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(=\sqrt{4+2\sqrt{2}}.\sqrt{2^2-2-\sqrt{2}}=\sqrt{2}.\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2}}\)
\(=\sqrt{2}.\sqrt{4-2}=\sqrt{2}.\sqrt{2}=2\)
\(C=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
\(=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2^2-\left(2+\sqrt{2+\sqrt{3}}\right)}\)
\(=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2-\sqrt{2+\sqrt{3}}}=\sqrt{2+\sqrt{3}}.\sqrt{2^2-\left(2+\sqrt{3}\right)}\)
\(=\sqrt{2+\sqrt{3}}.\sqrt{2-\sqrt{3}}=\sqrt{4-3}=1\)
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\(D=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(=\sqrt{4+\sqrt{15}}.\sqrt{2}.\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4+\sqrt{15}}.\sqrt{4-\sqrt{15}}\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}.\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4^2-15}\)
\(=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)=5-3=2\)
\(E=\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right).\sqrt{3-\sqrt{5}}\)
\(=\sqrt{3+\sqrt{5}}.\sqrt{3-\sqrt{5}}.\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}.\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}\)
\(=2\sqrt{3-\sqrt{5}}+2\sqrt{3+\sqrt{5}}=\sqrt{2}\left(\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}\right)\)
\(=\sqrt{2}.\left(\sqrt{5}-1+\sqrt{5}+1\right)=2\sqrt{10}\)
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TínhAleft(4+sqrt{15}right)left(sqrt{10}-sqrt{6}right)cdotsqrt{4-sqrt{15}}Bleft(3-sqrt{5}right)cdotsqrt{3+sqrt{5}}+left(3+sqrt{5}right)cdotsqrt{3-sqrt{5}}Csqrt{2+sqrt{3}}cdotsqrt{2+sqrt{2+sqrt{3}}}cdotsqrt{2+sqrt{2+sqrt{2+sqrt{3}}}}cdotsqrt{2-sqrt{2+sqrt{2+sqrt{ }}3}}Dsqrt{4+sqrt{15}}+sqrt{4-sqrt{15}}-2sqrt{3-sqrt{5}}Efrac{sqrt{15-10sqrt{2}}+sqrt{13+4sqrt{5}}-sqrt{11+2sqrt{10}}}{2sqrt{3+2sqrt{2}}+sqrt{9-4sqrt{2}}+sqrt{12+8sqrt{2}}}
Đọc tiếp
Tính
A=\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
B=\(\left(3-\sqrt{5}\right)\cdot\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\cdot\sqrt{3-\sqrt{5}}\)
C=\(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{ }}3}}\)
D=\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
E=\(\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{5}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
a: \(A=\left(4+\sqrt{15}\right)\cdot\left(\sqrt{5}-\sqrt{3}\right)\cdot\sqrt{8-2\sqrt{15}}\)
\(=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\)
\(=32-8\sqrt{15}+8\sqrt{15}-30=2\)
b: \(\sqrt{2}\cdot B=\left(3-\sqrt{5}\right)\left(\sqrt{5}+1\right)+\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\)
\(\Leftrightarrow B\sqrt{2}=3\sqrt{5}+3-5-\sqrt{5}+3\sqrt{5}-3+5-\sqrt{5}\)
\(\Leftrightarrow B\sqrt{2}=4\sqrt{5}\)
hay \(B=2\sqrt{10}\)
d: \(D\sqrt{2}=\sqrt{5}+\sqrt{3}+\sqrt{5}-\sqrt{3}-2\cdot\left(\sqrt{5}-1\right)\)
\(=2\sqrt{5}-2\sqrt{5}+2=2\)
hay \(D=\sqrt{2}\)
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BT: Tính
a, \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
b,\(\left(3-\sqrt{5}\right)\cdot\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\cdot\sqrt{3-\sqrt{5}}\)
c,\(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
https://i.imgur.com/LeR5GY4.jpg
a: \(=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\cdot\sqrt{8-2\sqrt{15}}\)
\(=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\)
\(=32-8\sqrt{15}+8\sqrt{15}-30=2\)
b: \(=\dfrac{\left(3-\sqrt{5}\right)\left(\sqrt{5}+1\right)+\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)}{\sqrt{2}}\)
\(=\dfrac{3\sqrt{5}+3-5-\sqrt{5}+3\sqrt{5}-3+5-\sqrt{5}}{\sqrt{2}}\)
\(=\dfrac{4\sqrt{5}}{\sqrt{2}}=2\sqrt{10}\)
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a) \(\left(2+\sqrt{3}\right)\cdot\sqrt{7-4\sqrt{3}}\)
b) \(\sqrt{4+2\sqrt{3}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}+\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
c) \(\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
\(\left(2+\sqrt{3}\right)\left(\sqrt{7-4\sqrt{3}}\right)=\left(2+\sqrt{3}\right)\sqrt{4-4\sqrt{3}+3}\)
\(=\left(2+\sqrt{3}\right).\sqrt{\left(2-\sqrt{3}\right)^2}\)
\(=\left(2+\sqrt{3}\right)\left|2-\sqrt{3}\right|\)
\(=\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)\)( Vì \(2-\sqrt{3}>0\))
\(=4-2=1\)
mk
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Thực hiện phép tính:a,left(sqrt{28}-2sqrt{14}+sqrt{7}right)cdotsqrt{7}+7sqrt{8}b,left(sqrt{8}-3sqrt{2}+sqrt{10}right)cdotleft(sqrt{2}-3sqrt{0.4}right)c,left(15sqrt{50}+5sqrt{200}-3sqrt{450}right):sqrt{10}d,sqrt{6+2sqrt{5}}+sqrt{6-2sqrt{5}}e,sqrt{11+6sqrt{2}}-sqrt{11-6sqrt{2}}f,sqrt[3]{5sqrt{2}+7}-sqrt[3]{5sqrt{2}-7}g,sqrt[3]{20+14sqrt{2}}+sqrt[3]{20-14sqrt{2}}h,sqrt[3]{26+15sqrt{3}}-sqrt[3]{26-15sqrt{3}}
Đọc tiếp
Thực hiện phép tính:
\(a,\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\cdot\sqrt{7}+7\sqrt{8}\)
\(b,\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\cdot\left(\sqrt{2}-3\sqrt{0.4}\right)\)
\(c,\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):\sqrt{10}\)
\(d,\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
\(e,\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(f,\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
\(g,\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}\)
\(h,\sqrt[3]{26+15\sqrt{3}}-\sqrt[3]{26-15\sqrt{3}}\)
g, h. Câu hỏi của Nữ hoàng sến súa là ta - Toán lớp 9 - Học toán với OnlineMath
Câu 1: Thực hiện phép tính
a,left(sqrt{12}+3sqrt{15}-4sqrt{135}right)cdotsqrt{3}
b,sqrt{252}-sqrt{700}+sqrt{1008}-sqrt{448}
c,2sqrt{40sqrt{12}}-2sqrt{sqrt{75}}-3sqrt{5sqrt{48}}
Câu 2: Rút gọn
a,frac{9sqrt{5}+3sqrt{27}}{sqrt{5}+sqrt{3}}
b,frac{3sqrt{8}+2sqrt{12}+sqrt{20}}{3sqrt{18}-2sqrt{27}+sqrt{45}}
c,left(4+sqrt{15}right)cdotleft(sqrt{10}-sqrt{6}right)cdotsqrt{4-sqrt{15}}
Câu 3:So sánh
a,3+sqrt{5}và2sqrt{2}+sqrt{6}
b,2sqrt{3}+4và3sqrt{2}+sqrt{10}
c,18vàsqrt{15}cdotsqrt{17}
Đọc tiếp
Câu 1: Thực hiện phép tính
\(a,\left(\sqrt{12}+3\sqrt{15}-4\sqrt{135}\right)\cdot\sqrt{3}\\ b,\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\\ c,2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)
Câu 2: Rút gọn
\(a,\frac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}\\ b,\frac{3\sqrt{8}+2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\\ c,\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
Câu 3:So sánh
\(a,3+\sqrt{5}và2\sqrt{2}+\sqrt{6}\\ b,2\sqrt{3}+4và3\sqrt{2}+\sqrt{10}\\ c,18và\sqrt{15}\cdot\sqrt{17}\)
rút gọnAleft(sqrt{28}-2sqrt{14}+sqrt{7}right)cdotsqrt{7}+7sqrt{8}Bsqrt{6+2sqrt{5}}-sqrt{6-2sqrt{5}}Cleft(sqrt{7}-sqrt{10}right)^2+sqrt{280}Ddfrac{sqrt{99}}{sqrt{11}}+sqrt{7}cdotsqrt{63}-sqrt{sqrt{81}}Esqrt{27}left(s-sqrt{5}right)^2cdotleft(3sqrt{48}right)giải chi tiết ra giúp mik nha,cảm ơn nhiều
Đọc tiếp
rút gọn
A=\(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\cdot\sqrt{7}+7\sqrt{8}\)
B=\(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
C=\(\left(\sqrt{7}-\sqrt{10}\right)^2+\sqrt{280}\)
D=\(\dfrac{\sqrt{99}}{\sqrt{11}}+\sqrt{7}\cdot\sqrt{63}-\sqrt{\sqrt{81}}\)
E=\(\sqrt{27}\left(s-\sqrt{5}\right)^2\cdot\left(3\sqrt{48}\right)\)
giải chi tiết ra giúp mik nha,cảm ơn nhiều
bài 1: tính
a) sqrt{1,2cdot27} b) sqrt{55cdot77cdot35}
c) (sqrt{3}-sqrt{2} )^2 d) (3sqrt{2}-1)*(3sqrt{2}+1)
e) (sqrt{6}+7) (sqrt{3}-sqrt{2}) i) sqrt{dfrac{1}{8}}cdotsqrt{2}cdotsqrt{125}cdotsqrt{dfrac{1}{5}}
h) sqrt{sqrt{2}-1}cdotsqrt{sqrt{2}}+1
bài 2: tính
a) sqrt{9}-sqrt{17}cdotsqrt{9}+sqrt{17}
b) 2sqrt{2}left(sqrt{3}-2right)+left(1+2sqrt{2}right)^2-2sqrt{6}
c) dfrac{sqrt{6}+sqrt{14}}{2sqrt{3}+sqrt{28}} d) dfrac{sqrt{10}+sqrt{15}}{sqrt{8}+sqrt{...
Đọc tiếp
bài 1: tính
a) \(\sqrt{1,2\cdot27}\) b) \(\sqrt{55\cdot77\cdot35}\)
c) (\(\sqrt{3}-\sqrt{2}\) )\(^2\) d) (3\(\sqrt{2}-1\))*(3\(\sqrt{2}+1\))
e) (\(\sqrt{6}+7\)) (\(\sqrt{3}-\sqrt{2}\)) i) \(\sqrt{\dfrac{1}{8}}\cdot\sqrt{2}\cdot\sqrt{125}\cdot\sqrt{\dfrac{1}{5}}\)
h) \(\sqrt{\sqrt{2}-1}\cdot\sqrt{\sqrt{2}}+1\)
bài 2: tính
a) \(\sqrt{9}-\sqrt{17}\cdot\sqrt{9}+\sqrt{17}\)
b) 2\(\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\)
c) \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\) d) \(\dfrac{\sqrt{10}+\sqrt{15}}{\sqrt{8}+\sqrt{12}}\)
e) \(\dfrac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}\) f) \(\dfrac{x+\sqrt{xy}}{9+\sqrt{xy}}\) (xy>0)
Bài 1:
a: \(=\sqrt{32.4}=\dfrac{9}{5}\sqrt{10}\)
b: \(=\sqrt{5\cdot5\cdot7\cdot7\cdot11\cdot11}=5\cdot7\cdot11=385\)
c: \(=5-2\sqrt{6}\)
d: \(=18-1=17\)
e: \(=3\sqrt{2}-2\sqrt{3}+7\sqrt{3}-7\sqrt{2}=-4\sqrt{2}+5\sqrt{3}\)
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Tính
a) \(\left(2-\sqrt{3}\right)\cdot\left(2+\sqrt{3}\right)\)
b) \(\left(2\sqrt{3}-\sqrt{5}\right)\cdot\left(2\sqrt{3}+\sqrt{5}\right)\)
a) \(\left(2-\sqrt{3}\right)\cdot\left(2+\sqrt{3}\right)\)
\(=2^2-\left(\sqrt{3}\right)^2\)
\(=4-3=1\)
b) \(\left(2\sqrt{3}-\sqrt{5}\right)\left(2\sqrt{3}+\sqrt{5}\right)\)
\(=\left(2\sqrt{3}\right)^2-\left(\sqrt{5}\right)^2\)
\(=12-5=7\)
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a) (2 - √3)(2 + √3)
= 2² - (√3)²
= 4 - 3
= 1
b) (2√3 - √5)(2√3 + √5)
= (2√3)² - (√5)²
= 12 - 5
= 7
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