\(\sqrt{4-\sqrt{9+4\sqrt{2}}}\\ =\sqrt{4-\sqrt{\left(2\sqrt{2}+1\right)^2}}\\ =\sqrt{4-2\sqrt{2}-1}\\ =\sqrt{3-2\sqrt{2}}\\ =\sqrt{\left(1-\sqrt{2}\right)^2}\\ =\sqrt{2}-1\)
CHÚC BẠN HỌC TỐT!
Giải các phương trình sau:
a)\(\sqrt[3]{9-x}+\sqrt[3]{7+x}=4\)
b)\(\sqrt{x-1}\cdot\sqrt[4]{x^2-4}=\sqrt{x-2}\cdot\sqrt[4]{x^2-1}\)
c)\(\sqrt[4]{9-x^2}+\sqrt{x^2-1}-2\sqrt{2}=\sqrt[6]{x-3}\)
\(\sqrt{3-2\sqrt{2}}-\sqrt{11+6\sqrt{2}}\)
\(\sqrt{4-2\sqrt{3}}-\sqrt{7-4\sqrt{3}}+\sqrt{19+8\sqrt{3}}\)
\(\sqrt{6-2\sqrt{5}}+\sqrt{9+4\sqrt{5}}-\sqrt{14-6\sqrt{5}}\)
\(\sqrt{11-4\sqrt{7}}+\sqrt{23-8\sqrt{7}}+\sqrt{\left(-2^6\right)}\)
rút gọn:giải chi tiết hộ mình nha
Tính
1/ \(\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
2/ \(\sqrt{17-6\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
3/ \(\sqrt{3+\sqrt{5-\sqrt{13+4\sqrt{3}}}}\)
4/ \(\sqrt{27+10\sqrt{2}}:\dfrac{1}{\sqrt{\left(\sqrt{2}-5\right)^2}}\)
Chứng minh:
\(\dfrac{a+\sqrt{2+\sqrt{5}}.\sqrt{\sqrt{9-4\sqrt{5}}}}{\sqrt[3]{2-\sqrt{5}}.\sqrt[3]{\sqrt{9+4\sqrt{5}}}-\sqrt[3]{a^2}+\sqrt[3]{a}}=-\sqrt[3]{a}-1\)
M=\(\sqrt{9+4\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
N=\(\sqrt{7-4\sqrt{3}}-\sqrt{12-6\sqrt{3}}\)
Rút gọn
a) \(\sqrt{\sqrt{2\sqrt{6}+6+2\sqrt{2}+2\sqrt{3}}-\sqrt{5+2\sqrt{6}}}\)
b) \(\sqrt{x^2-6x+9}-\dfrac{x^2-9}{\sqrt{9-6x+x^2}}\)
c) \(\dfrac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
d) Rút gọn \(A=\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\)với \(2\le x\le4\)
tính
\(\sqrt{9+4\sqrt{2}}+\sqrt{9-4\sqrt{2}}\)
a) \(\sqrt{3^2}-\sqrt{\left(7\right)^2}+\sqrt{\left(-1\right)^2}\)
b)\(-2\sqrt{\left(-2\right)^2}+\sqrt{\left(-5\right)^2}+\sqrt{3^2}\)
c)\(\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(2+\sqrt{2}\right)^2}\)
d)\(\sqrt{\left(3\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
e)\(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}\)
f)\(\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
g)\(\sqrt{9-4\sqrt{2}}+\sqrt{11-6\sqrt{2}}\)
h)\(\sqrt{12+8\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
k)\(\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}}\)
Tính (Rút gọn):
a) \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b)\(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)
c)\(\left(\sqrt{5+2\sqrt{9\sqrt{5}-19}}-\sqrt{7-\sqrt{5}}\right):2\sqrt{\sqrt{5}-2}\)
d)\(\frac{\sqrt{9+\sqrt{5}}+\sqrt{9-\sqrt{5}}}{\sqrt{9+2\sqrt{19}}}-\sqrt{3-2\sqrt{2}}\)
Rút gọn biểu thức:
a) \(\sqrt{9-2\sqrt{14}}\)
b) \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
c) \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
