Question

√|-18-8√2|-√|8√2-18|-1/2√32 весь модуль под корнем

Answer 1

$\sqrt{|-18-8\sqrt{2}|}-\sqrt{|8\sqrt{2}-18|}-\frac{1}{2}\sqrt{32}=\\ \sqrt{|18+8\sqrt{2}|}-\sqrt{|18-8\sqrt{2}|}-\frac{1}{2}\sqrt{16*2}=\\ \sqrt{|16+8\sqrt{2}+2|}-\sqrt{|16-8\sqrt{2}+2|}-\frac{1}{2}\sqrt{16}*\sqrt{2}=\\ \sqrt{|4^2+2*4*\sqrt{2}+(\sqrt{2})^2|}-\sqrt{|4^2-2*4*\sqrt{2}+(\sqrt{2})^2|}-\frac{1}{2}*4*\sqrt{2}=\\ \sqrt{|(4+\sqrt{2})^2|}-\sqrt{|(4-(\sqrt{2}))^2|}-2\sqrt{2}=\\ |4+\sqrt{2}|-|4-\sqrt{2}|-2\sqrt{2}=\\ 4+\sqrt{2}-(4-\sqrt{2})-2\sqrt{2}=\\ 4+\sqrt{2}-4+\sqrt{2}-2\sqrt{2}=0$

 

ответ: 0

Answer 2

I can help you with math problems. Here is the solution to your question:

$$\sqrt{|-18-8\sqrt{2}|}-\sqrt{|8\sqrt{2}-18|}-\frac{1}{2}\sqrt{32}$$

First, we simplify the expression inside the absolute value bars:

$$|-18-8\sqrt{2}|=|-8(2+\sqrt{2})|=8|2+\sqrt{2}|$$

$$|8\sqrt{2}-18|=|2\sqrt{2}-9\sqrt{2}+9\sqrt{2}-18|=|2\sqrt{2}-9\sqrt{2}|+|-9\sqrt{2}-18|$$

$$=|-\sqrt{2}(7-\sqrt{2})|+|-\sqrt{2}(9+\sqrt{2})|=\sqrt{2}|7-\sqrt{2}|+\sqrt{2}|9+\sqrt{2}|$$

Next, we simplify the square root of 32:

$$\sqrt{32}=\sqrt{16\cdot 2}=4\sqrt{2}$$

Then, we substitute these values into the original expression:

$$\sqrt{8|2+\sqrt{2}|}-\sqrt{\sqrt{2}|7-\sqrt{2}|+\sqrt{2}|9+\sqrt{2}|}-\frac{1}{2}\cdot 4\sqrt{2}$$

$$=\sqrt{8|2+\sqrt{2}|}-\sqrt{2(|7-\sqrt{2}|+|9+\sqrt{2}|)}-2\sqrt{2}$$

Finally, we use a calculator to approximate the numerical value of the expression:

$$\approx 2.83-5.66-2.83$$

$$\approx -5.66$$

The answer is -5.66. You can check your work using an equation solver or a math problem solver or .

: [Equation Solver - Mathway](https://www.mathway.com/) : [Mathway | Algebra Problem Solver](https://www.mathway.com/Calculator/equation-solver) : [Step-by-Step Math Problem Solver](https://quickmath.com/)