Tính $A=\sqrt{64}+\sqrt{16}-2 \sqrt{36}$.
Câu 1 (2 điểm).
a) Tính \(\sqrt{64}+\sqrt{16}-2\sqrt{36}\).
b) Rút gọn biểu thức P=\(\left(\dfrac{1}{\sqrt{x}}-\dfrac{2}{1+\sqrt{x}}\right).\dfrac{x+\sqrt{x}}{1-\sqrt{x}}\), với x>0; x\(\ne1\).
Câu 1 :
a, \(=8+4-2.6=12-12=0\)
b, đk : x > 0 ; x khác 1
\(P=\left(\dfrac{\sqrt{x}+1-2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\right).\dfrac{x+\sqrt{x}}{1-\sqrt{x}}=\dfrac{1-\sqrt{x}}{1-\sqrt{x}}=1\)
tính (-2)^2+\(\sqrt{\left(\frac{36}{49}\right)-\sqrt{16}+\sqrt{\left(\frac{64}{-2}\right)}}\)
Tính
a) \(2\sqrt{\frac{25}{16}}-3\sqrt{\frac{49}{36}}+4\sqrt{\frac{81}{64}}\)
b) \(\left(3\sqrt{2}\right)^2-\left(4\sqrt{\frac{1}{2}}\right)^2+\frac{1}{16}.\left(\sqrt{\frac{3}{4}}\right)^2\)
c) \(\frac{2}{3}\sqrt{\frac{81}{16}}-\frac{3}{4}\sqrt{\frac{64}{9}}+\frac{7}{5}.\sqrt{\frac{25}{196}}\)
a) = \(\frac{7}{2}\)
b) = \(\frac{643}{64}\)
c) = 0
Tính giá trị biểu thức:
\(A=\sqrt{8}+\sqrt{18}-\sqrt{32}\)
\(B=2\sqrt{9}+3\sqrt{36}-\sqrt{64}\)
\(A=2\sqrt{2}+3\sqrt{2}-4\sqrt{2}=\sqrt{2}\)
B=6+18-8=16
\(A=2\sqrt{2}+3\sqrt{2}-4\sqrt{2}=\sqrt{2}\\ B=2\cdot3+3\cdot6-8=6+18-8=16\)
a =2 \(\sqrt{2}\) + 3\(\sqrt{2}\)- 4\(\sqrt{2}\)
=\(\sqrt{2}\)
Tính
a) \(2\sqrt{\dfrac{25}{16}}-3\sqrt{\dfrac{49}{36}}+4\sqrt{\dfrac{81}{64}}\)
b) \(\left(3\sqrt{2}\right)^2-\left(4\sqrt{\dfrac{1}{2}}\right)^2+\dfrac{1}{16}.\left(\sqrt{\dfrac{3}{4}}\right)^2\)
c) \(\dfrac{2}{3}\sqrt{\dfrac{81}{16}}-\dfrac{3}{4}\sqrt{\dfrac{64}{9}}+\dfrac{7}{5}.\sqrt{\dfrac{25}{196}}\)
a: \(=2\cdot\dfrac{5}{4}-3\cdot\dfrac{7}{6}+4\cdot\dfrac{9}{8}=\dfrac{5}{2}-\dfrac{7}{2}+\dfrac{9}{2}=\dfrac{7}{2}\)
b: \(=18-16\cdot\dfrac{1}{2}+\dfrac{1}{16}\cdot\dfrac{3}{4}\)
=10+3/64
=643/64
c: \(=\dfrac{2}{3}\cdot\dfrac{9}{4}-\dfrac{3}{4}\cdot\dfrac{8}{3}+\dfrac{7}{5}\cdot\dfrac{5}{14}=\dfrac{3}{2}-2+\dfrac{1}{2}=2-2=0\)
Cho\(\sqrt{x^2-6x+36}+\sqrt{x^2-6x+64}=18\)
Tính: \(\sqrt{x^2-6x+64}-\sqrt{x^2-6x+36}\)
Đặt \(A=\sqrt{x^2-6x+36}+\sqrt{x^2-6x+64}=18\)
\(B=\sqrt{x^2-6x+64}-\sqrt{x^2-6x+36}\)
\(\Rightarrow A.B=\left(x^2-6x+64\right)-\left(x^2-6x+36\right)=28\)
mà \(A=18\Rightarrow B=\frac{28}{18}=\frac{14}{9}\)
Giá trị biểu thức A = [ \(\sqrt{64}\) + 2.\(\sqrt{(-3)^{2}}\)- 7.\(\sqrt{1,69}\) + 3.\(\sqrt{\dfrac{25}{16}}\)] : (5.\(\sqrt{\dfrac{2}{3}})^{2}\)
Tính A. Các bạn giúp mk với ạ.
\(A=\left(8+2\cdot3-7\cdot\dfrac{13}{10}+3\cdot\dfrac{5}{4}\right):\left(\dfrac{5\sqrt{6}}{3}\right)^2\\ A=\left(14-\dfrac{91}{10}+\dfrac{15}{4}\right):\dfrac{50}{3}\\ A=\dfrac{173}{20}\cdot\dfrac{3}{50}=\dfrac{519}{1000}\)
Rút gọn các biểu thức sau:
a) $M=\sqrt{4(x-1)}-\sqrt{9(x-1)}-\sqrt{16(x-1)}$ với $x \geq 1$;
b) $N=\sqrt{25(y+4)}+\sqrt{36(y+4)}-2 \sqrt{81(y+4)}$ với $y \geq-4$;
c) $P=\sqrt{(y-2)}-3 \sqrt{64(y-2)}+4 \sqrt{49(y-2)}$ với $y \geq 2$.
a) \(M=\sqrt{4\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{16\left(x-1\right)}\)
\(=2\sqrt{x-1}-3\sqrt{x-1}-4\sqrt{x-1}=-5\sqrt{x-1}\)
b) \(N=\sqrt{25\left(y+4\right)}+\sqrt{36\left(y+4\right)}-2\sqrt{81\left(y+4\right)}\)
\(=5\sqrt{y+4}+6\sqrt{y+4}-18\sqrt{y+4}=-7\sqrt{y+4}\)
c) \(P=\sqrt{y-2}-3\sqrt{64\left(y-2\right)}+4\sqrt{49\left(y-2\right)}\)
\(=\sqrt{y-2}-24\sqrt{y-2}+28\sqrt{y-2}=5\sqrt{y-2}\)
a) \(M=\sqrt{4\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{16\left(x-1\right)}.\)
\(M=\sqrt{4\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{16\left(x-1\right)}\)
\(=2\sqrt{x-1}-3\sqrt{x-1}-4\sqrt{x-1}\)
\(=-5\sqrt{x-1}\)
b) \(N=\sqrt{25\left(y+4\right)}+\sqrt{36\left(y+4\right)}-2\sqrt{81\left(y+4\right)}\)
\(N=\sqrt{25\left(y+4\right)}+\sqrt{36\left(y+4\right)}-2\sqrt{81\left(y+4\right)}\)
\(=5\sqrt{y+4}+6\sqrt{y+4}\)
\(=-7\sqrt{y+4}\)
c) \(P=\sqrt{\left(y-2\right)}-3\sqrt{64\left(y-2\right)}+4\sqrt{49\left(y-2\right)}\)
\(P=\sqrt{\left(y-2\right)}-3\sqrt{64\left(y-2\right)}+4\sqrt{49\left(y-2\right)}\)
\(=\sqrt{y-2}-24\sqrt{y-2}+28\sqrt{y-2}\)
\(=5\sqrt{y-2}\)
M=-5√(x-1)
N=-7√(y+4)
P=-2√(y-2)
Cho số thực x thỏa mãn \(\sqrt{x^2-6x+36}+\sqrt{x^2-6x+64}=18\)
Tính giá trị biểu thức \(A=\sqrt{4x^2-24x+256}-2\sqrt{x^2-6x+36}\)