Question

√75 - 2 √3 (3-6√12) + 14. решите с подробным объяснением

Answer 1

Ответ:$-обозначу так корень ( пишу ответ с телефона тут нет знака корня)

Объяснение:$25*3-2*3$3+2*6$12*3+14=5$3-6$3+12*3*2+14=-$3+86. 75=25*3; затем раскрываем скобки ; $12=$3*4

Answer 2

To solve the expression √75 - 2√3(3 - 6√12) + 14, we need to follow these steps:

Step 1: Simplify the expression within parentheses. Step 2: Perform any remaining operations involving square roots. Step 3: Combine like terms.

Let's start with Step 1:

Step 1: Simplify the expression within parentheses. Inside the parentheses, we have 3 - 6√12. To simplify this further, let's determine the value of √12:

√12 = √(4 * 3) = √4 * √3 = 2√3

So, 3 - 6√12 = 3 - 6 * 2√3.

Now, let's perform the subtraction:

3 - 6 * 2√3 = 3 - 12√3

Now, we have √75 - 2√3(3 - 12√3) + 14.

Step 2: Perform any remaining operations involving square roots.

Now, we have to distribute the -2√3 across the expression within parentheses:

-2√3(3 - 12√3) = -2√3 * 3 + -2√3 * (-12√3) = -6√3 + 24√3 = 18√3

So the expression becomes √75 + 18√3 + 14.

Step 3: Combine like terms.

Now, we need to combine the constant terms (those without square roots) and the square root terms separately:

Constant terms: 14 Square root terms: √75 + 18√3

However, we can still simplify further. Let's simplify the square root term:

√75 = √(25 * 3) = √25 * √3 = 5√3

So the square root term becomes 5√3 + 18√3 = 23√3.

Finally, the expression becomes:

14 + 23√3

This is the simplified form of the expression √75 - 2√3(3 - 6√12) + 14.