Đưa thừa số ra ngoài dấu căn :
a. \(\sqrt{9\text{6}}.\sqrt{\text{1}2\text{5}}\)
b.\(\sqrt{a^4.\text{6}^{\text{5}}}\)
c.\(\sqrt{a^{\text{6}}.b^{\text{1}\text{1}}}\)
d.\(\:\sqrt{a^{\text{3}}\left(\text{1}-a\right)^4}\)
\(Cho\text{ }x,y,z\text{ }\in R\text{ thỏa}\text{ }xyz=1.\text{Tìm Min:}\)
\(P=\left(\left|xy\right|+\left|yz\right|+\left|zx\right|\right)\left[15\sqrt{x^2+y^2+z^2}-7\left(x+y-z\right)\right]+1\)
\(\text{Cho x,y,z }\in R\text{ thỏa mãn điều kiện }xyz=1\text{.Tìm Min:}\)
\(P=\left(\left|xy\right|+\left|yz\right|\left|zx\right|\right).\left[15\sqrt{x^2+y^2+z^2}-7\left(x+y-z\right)\right]+1\)
Rút gọn:
a)\(\sqrt{\left(\sqrt{7-2}\right)^2}\)
b)\(\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(2-3\sqrt{2}\right)^2}\)
c)\(\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
d) \(\sqrt{2+\sqrt{3}}+\sqrt{2a-3}\)
e)\(\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}+\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}\)
f)\(\sqrt{9a^{ }2}+3a-7\left(v\text{ơ}\text{í}a< 0\right)\)
g) \(\dfrac{\sqrt{4x^2-4x+1}}{4x-2}+3x+2\)(vơí x>\(\dfrac{1}{2}\))
h)\(\sqrt{\left(5a-1\right)^2}+2a-3\)
i)\(\sqrt{\dfrac{2a}{5}}.\sqrt{\dfrac{5a}{18}+}2\left(a-1\right)\)(vơí a>=0)
Cho P =( \(\frac{2\text{x}\sqrt{x}+x-\sqrt{x}}{x\sqrt{x}-1}-\frac{x+\sqrt{x}}{x-1}\)) . \(\frac{x-1}{2\text{x}+\sqrt{x}-1}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
Rút gọn P
Bài 1 :Tìm x để căn thức có nghĩa
a) \(\sqrt{-2\text{x}+3}\)
b)\(\sqrt{\frac{-5}{x^2+6}}\)
c)\(\sqrt{\frac{4}{x+3}}\)
Bài 2 : Rút gọn
a)\(\sqrt{\left(4+\sqrt{2}\right)^2}\)
b) 2\(\sqrt{3}\) + \(\sqrt{\left(2-\sqrt{3}\right)^2}\)
c) \(\sqrt{\left(3-\sqrt{3}\right)^2}\)
Bài 3
a) \(\sqrt{9-4\sqrt{5}}\) - \(\sqrt{5}\) = -2
b) \(\sqrt{23+8\sqrt{7}}\) - \(\sqrt{7}\) = 4
c) \(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
Bài 4 : Rút gọn
a) \(\frac{x^2-5}{x+\sqrt{5}}\) với x khác \(\sqrt{5}\)
b) \(\frac{x^2+2\sqrt{2}+2}{x^2-2}\)
c) x - 4 +\(\sqrt{16-8\text{x}+x^2}\) với x >4
Tính \(\dfrac{2-\sqrt{2\text{+}\sqrt{2\text{+}\sqrt{2\text{+}\sqrt{2}}}}}{2-\sqrt{2\text{+}\sqrt{2\text{+}\sqrt{2}}}}\)
\(\sqrt{\text{x+4}}\)+\(2\sqrt{\text{x+1}}\)=\(\sqrt{\text{x+20}}\)
M=\(\text{[}\dfrac{\sqrt{a}}{2}-\dfrac{1}{2\sqrt{a}\text{ư}}\text{]}\text{[}\dfrac{a-\sqrt{a}}{\sqrt{a+1}}-\dfrac{a+\sqrt{a}}{\sqrt{a}-1}\text{]}\)
a)Tìm ĐKXĐ của M
b) Rút gọn M
c) Tìm giá trị của a để M=-4
Dấu ngoặc tròn chứ không phải ngoặc vuông nha
