\(A=\sqrt{\dfrac{4+\sqrt{7}}{2}}-\dfrac{1}{2}=\sqrt{\dfrac{8+2\sqrt{7}}{4}}-\dfrac{1}{2}\)
\(=\dfrac{\sqrt{7}+1}{2}-\dfrac{1}{2}=\dfrac{\sqrt{7}}{2}\)
\(B=3+\dfrac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}=3+\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)\)
\(=3+3-\sqrt{6}=6-\sqrt{6}\)
1 trên căn x ccongj ba cộng với 1 trên căn x trừ ba nhân với 1 trừ đi 3 trên căn x
Tính
a,(√5+√3+1)×(√5-1)
b,(5-2√3)×(5+2√3)
c,1/3×√15:3/4×√3×4√2×7√10
d,(10√48-6√27+4√12):√3
Bài tập: Thực hiện phép tính
\(\left(\dfrac{1}{3}\sqrt{\dfrac{1}{2}}-\dfrac{2}{3}\sqrt{\dfrac{1}{3}}+\dfrac{2}{7}\sqrt{\dfrac{4}{5}}\right):\left(\dfrac{2}{7}\sqrt{\dfrac{1}{8}}\right)\)
1, 1+\(\sqrt{\text{6}+2\sqrt{5}}\)
2, \(\sqrt{\text{7}-2\sqrt{\text{10}}}\) +\(\sqrt{\text{2}}\)
3, \(\sqrt{\text{7}+4\sqrt{3}}\)
Tính:
A=\(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
B=\(\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
C=\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
D=\(\sqrt{5\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
E=\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)(2 cách)
F=\(\dfrac{\sqrt{17-12\sqrt{2}}}{\sqrt{3-2\sqrt{2}}}-\dfrac{\sqrt{17}+12\sqrt{2}}{\sqrt{3+2\sqrt{2}}}\)
A\(=\)\((3\sqrt{8}+2\sqrt{50}-4\sqrt{72})\)\(➗\)\(8\sqrt{2}\)
B\(=\)\((-4\sqrt{20}+5\sqrt{500}-3\sqrt{45})\div5 \)
C\(=(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}-\dfrac{\sqrt{3}-1}{\sqrt{3}+1})\div\sqrt{48}\)
Bài1: Tính
a) \(\sqrt{4-\sqrt{15}}+\sqrt{2-\sqrt{3}}\)
b) \(\sqrt{4-\sqrt{7}}+\sqrt{8-3\sqrt{7}}\)
BT1: Tính
a, \(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
b, \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
BT2: Rút gọn
\(3x-\sqrt{27}+\frac{\sqrt{x^3+3x^2}}{\sqrt{x+3}}\) ( x ≥ 0 )
Tính : a)\(\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}-\dfrac{3}{3-\sqrt{6}}\)
b)\(\left(2\sqrt{2}-\sqrt{3}\right)^2-2\sqrt{3}\left(\sqrt{3}-2\sqrt{2}\right)\)
c) \(\left(\dfrac{1}{3-\sqrt{5}}-\dfrac{1}{3+\sqrt{5}}\right):\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\)
d)\(\left(3-\dfrac{a-2\sqrt{a}}{\sqrt{a}-2}\right)\left(3+\dfrac{\sqrt{ab}-3\sqrt{a}}{\sqrt{b}-3}\right)\)b \(\ne\) 9 với a\(\ge\)0 , b\(\ge\)0, a\(\ne\) 4
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