Question

1.найдите значение выражения (8√12+4√75):3√3 1)116 2)4 3)36 4)12 2. Упростите выражение :а(а-4)-(а-2)^2. 1)2а^2 2)4-а^2 3)а^2-4 4)-4 3.из формулы y= ax/3 выразите х. 1))х=3у/а 2)х=3а/у 3)х=а-3/у 4)х=а/3у 4.вычислите : √3 ×√8×√6/√4 1)24 2)12 3)3 4)6 5.выполните деление дробей :6х +6у/х : х^2-у^2/х^2.

Answer 1

V обозначает корень

1. (8v12 +4v75) :3v3 =(8v(3*2²) +4v(3*5²)) :3v3 =(8*2v3 +4*5v3) :3v3 =(16v3 +20v3) :3v3 =36v3 /3v3 =36/3 =12
ответ: номер 4

2. a) a(a -4) -(a -2)² =a² -4a -(a² -4a +4) =a² -4a -a² +4a -4 = -4
ответ: номер 4

3. y =ax/3
3y =ax
x =3y/a
ответ: 1

4. (v3 *v8 *v6) /v4 =v(3*8*6) /v4 =v144 /v4 =v12² /v2² =12/2 =6
ответ: номер 4

5. (6x+6y)/x : (x² -y²)/x² =6(x+y)/x * x²/(x -y)(x+y) =6x²(x+y) /x(x -y)(x+y) =6x/(x-y)

Answer 2

Question: Find the value of the expression (8√12+4√75):3√3+1)

To find the value of the expression, we need to simplify it step by step.

First, let's simplify the numerator: - 8√12 can be simplified as 8 * √(4 * 3) = 8 * √4 * √3 = 8 * 2 * √3 = 16√3 - 4√75 can be simplified as 4 * √(25 * 3) = 4 * √25 * √3 = 4 * 5 * √3 = 20√3

So the numerator becomes 16√3 + 20√3 = 36√3

Next, let's simplify the denominator: - 3√3 remains as it is.

Now, let's simplify the entire expression: (8√12+4√75):3√3+1 = (36√3):3√3 + 1

Since the denominator and the numerator have the same value, we can simplify it as: (36√3):3√3 + 1 = 36:3 + 1 = 12 + 1 = 13

So the value of the expression is 13.

2. Simplify the expression: а(а-4)-(а-2)^2

To simplify the expression, we can start by expanding the squared term and then combining like terms.

Expanding the squared term: (а-2)^2 = (а-2)(а-2) = а(а-2) - 2(а-2) = а^2 - 2а - 2а + 4 = а^2 - 4а + 4

Now let's simplify the entire expression: а(а-4) - (а-2)^2 = а^2 - 4а - (а^2 - 4а + 4)

Removing the parentheses and combining like terms: а^2 - 4а - а^2 + 4а - 4 = -4

So the simplified expression is -4.

3. Express x in terms of y from the equation y = ax/3

To express x in terms of y, we need to isolate x on one side of the equation.

Starting with the given equation: y = ax/3

To isolate x, we can multiply both sides of the equation by 3: 3y = ax

Next, we can divide both sides of the equation by a: (3y)/a = x

So, x = (3y)/a

Therefore, we have expressed x in terms of y as x = (3y)/a.

4. Evaluate: √3 × √8 × √6 / √4

To evaluate this expression, we can simplify the square roots and then perform the multiplication and division.

Simplifying the square roots: √3 = √(3) = √(3) √8 = √(4 * 2) = √(4) * √(2) = 2√(2) √6 = √(2 * 3) = √(2) * √(3) = √(2)√(3) √4 = 2

Now let's substitute these values back into the expression: √3 × √8 × √6 / √4 = √(3) * 2√(2) * √(2)√(3) / 2

Combining like terms: = 2 * 2 * √(3) * √(2) * √(2) * √(3) / 2

Simplifying: = 4 * 3 * 2 = 24

Therefore, the value of the expression is 24.

5. Divide the fractions: (6x + 6y) / x : (x^2 - y^2) / x^2

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

The division of fractions (a/b) : (c/d) can be rewritten as (a/b) * (d/c).

Therefore, (6x + 6y) / x : (x^2 - y^2) / x^2 becomes (6x + 6y) / x * x^2 / (x^2 - y^2).

Next, let's simplify the expression: (6x + 6y) / x * x^2 / (x^2 - y^2)

We can cancel out common factors between the numerator and the denominator: (6(x + y)) * (x * x) / (x * (x + y)(x - y))

Simplifying further: 6x^2 / (x * (x - y))

Canceling out the common factor of x: 6x / (x - y)

Therefore, the simplified expression is 6x / (x - y).