Radicals equations-negative square root and two radicals

In summary, the conversation discusses the solution to the radical equations sqrt -81y^3 and sqrt 2n-5 - sqrt 3n+4=2. The conclusion is that there are no real solutions for these equations, and WolframAlpha can be used to verify this. The simplification of sqrt -81y^3 to |y|sqrt-81y is also mentioned.
  • #1
Coco12
272
0
Is the answer to sqrt -81y^3 : y sqrt-81y? or is there no real solutions?

Also for this radical equation:
sqrt 2n-5 - sqrt 3n+4=2
I worked it out and can't seem to get an answer. Is there no real solutions?
 
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  • #2
if y<0, then ##\sqrt{-81y^3}=|y|\sqrt{-81y}##, otherwise the square root is not defined in the real numbers.

Your equation has no real solutions. You can check this with WolframAlpha, for example.
 
  • #3
thank you so much, that WolframAlpha thing is very useful!
 
  • #4
That [itex] \sqrt{-81 y} [/itex] can be further simplified by noting that 92 = 81 and -y = |y| , for y smaller or equal to 0.
 

1. What are radicals in equations?

Radicals are mathematical expressions that contain a root sign (√) and a number or variable inside it. They are used to represent numbers that are not perfect squares, such as √2 or √x.

2. How do I solve equations with negative square roots?

To solve equations with negative square roots, you need to first isolate the square root term on one side of the equation. Then, square both sides of the equation to eliminate the square root. Finally, solve for the variable by following the basic rules of algebra.

3. Can an equation have two radicals?

Yes, an equation can have two radicals. This is known as a radical equation. To solve these equations, you need to isolate one radical at a time and follow the steps mentioned in the previous question.

4. What is the difference between a positive and negative square root?

The positive square root of a number is the number that, when multiplied by itself, gives the original number. The negative square root, on the other hand, is the opposite value of the positive square root. For example, the positive square root of 9 is 3, and the negative square root is -3.

5. How are radicals used in real-life applications?

Radicals are used in various fields, such as engineering, physics, and finance, to represent quantities that are not perfect squares. They are also used in geometry to find the length of a side in a right triangle or the distance between two points on a coordinate plane.

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