Question

БЛАГАЮ ВАС ЛЮДИ ДОБРІ поможіть даю 50+ балів, дуже треба Чому дорівнює значення виразу?1)2√(-15)²2)3√1,2²3)√6⁴4)√-2^105)5√(-10)⁴6)-4√(-1)¹⁴7)-10√3^6?​

Answer 1

Ответ:

Пользуемся формулами:  $\sqrt{A^2}=|A|=\left\{\begin{array}{l}A\ ,\ esli\ A\geq 0\ ,\\-A\ ,\ esli\ A$    

$1)\ \ 2\sqrt{(-15)^2}=2\cdot |-15|=2\cdot 15=30\\\\ili\ \ \ \ 2\sqrt{(-15)^2}=2\sqrt{225}=2\sqrt{15^2}=2\cdot 15=30\\\\2)\ \ 3\sqrt{1,2^2}=3\cdot |1,2|=3\cdot 1,2=3,6\\\\3)\ \ \sqrt{6^4}=\sqrt{(6^2)^2}=|6^2|=|36|=36\\\\4)\ \ \sqrt{-2^{10}}$

Так как $-2^{10}=-(2^{10})=-1024$  , a под знаком квадратного корня не может стоять отрицательное число, то такое выражение не имеет смысла .  Замечание:  не путать  $-2^{10}=-1024$  и  $(-2)^{10}=+1024$  .

$5)\ \ 5\sqrt{(-10)^4}=5\cdot \sqrt{10^4}=5\cdot \sqrt{(10^2)^2}=5\cdot \sqrt{100^2}=5\cdot |100|=5\cdot 100=500\\\\6)\ \ -4\sqrt{(-1)^{14}}=-4\sqrt{1}=-4\cdot 1=-4\\\\7)\ \ -10\sqrt{3^6}=-10\sqrt{(3^3)^2}=-10\sqrt{27^2}=-10\cdot |27|=-10\cdot 27=-270$

Answer 2

Calculating the Values of the Expressions

1) 2√(-15)² - The value of this expression can be calculated by first evaluating the square of -15 and then taking the square root of the result.

2) 3√1,2² - To find the value of this expression, we need to first square 1.2 and then take the cube root of the result.

3) √6⁴ - This expression requires us to calculate the square root of 6 raised to the power of 4.

4) √-2^10 - Here, we need to calculate the square root of -2 raised to the power of 10.

5) 5√(-10)⁴ - The value of this expression can be found by first raising -10 to the power of 4 and then taking the fifth root of the result.

6) -4√(-1)¹⁴ - This expression involves taking the fourteenth root of -1 and then multiplying the result by -4.

7) -10√3^6 - To calculate the value of this expression, we need to first raise 3 to the power of 6 and then take the tenth root of the result.

I will now calculate the values of these expressions using the given operations and numbers.

Calculated Values

1) 2√(-15)² - The value of this expression is 30. -

2) 3√1,2² - The value of this expression is approximately 1.5874. -

3) √6⁴ - The value of this expression is 36. -

4) √-2^10 - The value of this expression is 1024i (where i is the imaginary unit). -

5) 5√(-10)⁴ - The value of this expression is 100. -

6) -4√(-1)¹⁴ - The value of this expression is -4. -

7) -10√3^6 - The value of this expression is approximately -729.92. -

I hope these calculated values help! If you have any more questions or need further assistance, feel free to ask.