Question

Упростите выражение:

sqrt(12y)-0,5sqrt(48y)+2sqrt(108y)

(5sqrt(7)-sqrt(63)+sqrt(14))*sqrt(7)

Выполните действие:

(2+sqrt(3))(1-sqrt(3))

(sqrt(14)+2)(2-sqrt(14))

(1-2sqrt(3))^2

Сократите дробь:

5-sqrt(5)/2sqrt(5)

a^2-3/a+sqrt(3)

Answer 1

$\sqrt{12y}-0,5\sqrt{48y}+2\sqrt{108y}=\\ \sqrt{4*3y}-0,5\sqrt{16*3y}+2\sqrt{36*3y}=\\ \sqrt{4}*\sqrt{3y}-0,5\sqrt{16}*\sqrt{3y}+2\sqrt{36}*\sqrt{3y}=\\ 2*\sqrt{3y}-0,5*4*\sqrt{3y}+2*6*\sqrt{3y}=\\ (2-2+12)*\sqrt{3y}=\\ 12\sqrt{3y}$

 

$(5\sqrt 7-\sqrt {63}+\sqrt{14})*\sqrt7=\\ 5\sqrt 7 *\sqrt7-\sqrt {7*9}*\sqrt7+\sqrt{2*7}*\sqrt7=\\ 5*7-3*\sqrt {7}*\sqrt7+\sqrt{2}*\sqrt7*\sqrt7=\\ 35-3*7+7\sqrt{2}=\\ 35-21+7\sqrt{2}=14+7\sqrt{2}$

 

$(2+\sqrt{3})(1-\sqrt{3})=\\ 2-2\sqrt{3}+\sqrt{3}-3=-1-\sqrt{3}$

 

$(\sqrt{14}+2)(2-\sqrt{14})=\\ 2^2-(\sqrt{14})^2=4-14=-10$

 

$(1-2\sqrt{3})^2=1-4\sqrt{3}+4*3=13-4\sqrt{3}$

 

$\frac{5-\sqrt{5}}{2\sqrt{5}}=\\ \frac{\sqrt{5}(\sqrt{5}-1}{2\sqrt{5}}=\\ \frac{\sqrt{5}-1}{2}$

 

$\frac{a^2-3}{a+\sqrt{3}}=\\ \frac{(a+\sqrt{3})(a-\sqrt{3})}{a+\sqrt{3}}=a-\sqrt{3}$