Math Problem Statement

√x²/√x +2/√x=

Solution

The expression you've provided is:

x2x+2x\frac{\sqrt{x^2}}{\sqrt{x}} + \frac{2}{\sqrt{x}}

Let's simplify it step by step.

  1. Simplifying the first term: x2x\frac{\sqrt{x^2}}{\sqrt{x}}

    • x2=x\sqrt{x^2} = x, so this becomes xx\frac{x}{\sqrt{x}}.
    • xx=x\frac{x}{\sqrt{x}} = \sqrt{x} (because x=xxx = \sqrt{x} \cdot \sqrt{x}).
  2. Simplifying the second term: 2x\frac{2}{\sqrt{x}}

    This term stays as it is.

Now the expression is:

x+2x\sqrt{x} + \frac{2}{\sqrt{x}}

This is the simplified form of your expression.

If you'd like to further manipulate it or solve for specific values, feel free to ask!


Do you have any questions or would you like more details?
Here are 5 related questions you might find helpful:

  1. How do you rationalize a denominator with a square root?
  2. Can this expression be simplified further if given specific values for xx?
  3. What happens if xx is a negative number in this context?
  4. How does simplifying square roots work for more complex expressions?
  5. Can this expression be rewritten as a single fraction?

Tip: Whenever simplifying expressions with square roots, look for opportunities to cancel terms or combine like terms to make the expression more manageable!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Expressions
Square Roots
Radicals

Formulas

√(x²) = x
x = √(x) * √(x)

Theorems

Basic properties of square roots
Simplification of radicals

Suitable Grade Level

Grades 8-10