\(\left(3\sqrt{5}+3\sqrt{3}\right).\left(\sqrt{5}-\sqrt{3}\right)\)
= \(3\left(\sqrt{5}+\sqrt{3}\right).\left(\sqrt{5}-\sqrt{3}\right)\)
= \(3\left(5-3\right)\)
= 6
Tính:
1.\(\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\) 4.\(\sqrt{\left(\sqrt{3}\right)^2+2.\left(\sqrt{3}\right).\left(1\right)+\left(1\right)^2}\)
2.\(\sqrt{\left(\sqrt{5}-\sqrt{6}\right)^2}\) 5.\(\sqrt{\left(\sqrt{5}\right)^2+2.\left(\sqrt{5}\right).\left(\sqrt{3}\right)+\left(\sqrt{3}\right)^2}\)
3.\(\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}\) 6.\(\sqrt{\left(\sqrt{6}\right)^2-2.\left(\sqrt{6}\right).\left(\sqrt{5}\right)+\left(\sqrt{5}\right)^2}\)
Rút gọn :
a) \(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-2\right)\left(\sqrt{2+\sqrt{3}}\right)\)
b) \(\sqrt{2}.\left(\sqrt{2-\sqrt{3}}\right).\left(\sqrt{3}+1\right)\)
c) \(\left(\sqrt{10}-\sqrt{6}\right).\left(\sqrt{4-\sqrt{15}}\right)\)
d)\(\left(\sqrt{3}-\sqrt{12}\right).\left(\sqrt{5+2\sqrt{6}}\right)\)
e) \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}-\sqrt{2}\right).\left(2+\sqrt{3}\right)\)
f) \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
Rút gọn :
\(\dfrac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
b)\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)
c)\(\left(\sqrt{5}+1\right)\left(\sqrt{7}+1\right)\left(\sqrt{35}+1\right)\left(34-4\sqrt{7}-6\sqrt{5}\right)\)
d) \(\left(\sqrt{7}+1\right)\left(2\sqrt{2}-1\right)\left(2\sqrt{14}-1\right)\left(55+12\sqrt{2}-7\sqrt{7}\right)\)
e)\(\left(3\sqrt{2}+1\right)\left(2\sqrt{3}+1\right)\left(6\sqrt{6}+1\right)\left(215-34\sqrt{3}-33\sqrt{2}\right)\)
Tính:
a) \(\left(\sqrt{1\dfrac{9}{16}}-\sqrt{\dfrac{9}{16}}\right):5\)
b) \(\left(\sqrt{3}-2\right)^2\left(\sqrt{3}+2\right)^2\)
c) \(\left(11-4\sqrt{3}\right)\left(11+4\sqrt{3}\right)\)
d) \(\left(\sqrt{2}-1\right)^2-\dfrac{3}{2}\sqrt{\left(-2\right)^2}+\dfrac{4\sqrt{2}}{5}+\sqrt{1\dfrac{11}{25}}.\sqrt{2}\)
e) \(\left(1+\sqrt{2021}\right)\sqrt{2022-2\sqrt{2021}}\)
Thực hiện các phép tính (không được ghi mỗi kết quả không, phải giải chi tiết)
A = \(2\sqrt{10}.3\sqrt{8}.2\)
B = \(\sqrt{20}\left(2\sqrt{3}-\sqrt{5}\right)\)
C = \(\left(2\sqrt{5}-3\right)\left(2\sqrt{5}+3\right)\)
Thực hiện phép tính
a) \(\left(4+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b) \(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
c) \(\frac{\sqrt{\sqrt{5+2}}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+2}}-\sqrt{3-2\sqrt{2}}\)
Rút gọn biểu thức
a)\(\sqrt{26+15\sqrt{3}}\).
b)\(\sqrt{2-\sqrt{3}}\)
c)\(\left(\sqrt{10}-\sqrt{2}\right)\left(\sqrt{3+5}\right)\)
d)\(\left(\sqrt{6}-2\right)\left(5+\sqrt{24}\right)\sqrt{5-\sqrt{24}}\)
Rút gọn rồi tính:
a) \(5\sqrt{\left(-2\right)^4}\) c)\(\sqrt{\sqrt{\left(-5\right)^8}}\)
b)\(-4\sqrt{\left(-3\right)^6}\)
Tính :
\(\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\)
