Math Problem Statement

fraction sqaure root2/-3 + sqaure root 2

Solution

It seems like you're trying to express a mathematical expression involving square roots and fractions. Here's a more structured interpretation of the expression:

23+2\frac{\sqrt{2}}{-3} + \sqrt{2}

Let's break this down:

  1. First term: 23\frac{\sqrt{2}}{-3}
    This is simply the square root of 2 divided by -3.

  2. Second term: 2\sqrt{2}
    This is just the square root of 2.

Simplifying the expression:

23+2\frac{\sqrt{2}}{-3} + \sqrt{2}

We can rewrite the second term with a denominator of -3 to combine them:

2=2×(3)3=323\sqrt{2} = \frac{\sqrt{2} \times (-3)}{-3} = \frac{-3\sqrt{2}}{-3}

Now the expression looks like:

23+323\frac{\sqrt{2}}{-3} + \frac{-3\sqrt{2}}{-3}

Since both terms have the same denominator, we can combine them:

2323=223\frac{\sqrt{2} - 3\sqrt{2}}{-3} = \frac{-2\sqrt{2}}{-3}

Now, the negative signs cancel out:

223\frac{2\sqrt{2}}{3}

Final answer:

223\frac{2\sqrt{2}}{3}


Would you like a more detailed breakdown of any part of this? Or do you have any other questions?

Here are some related questions:

  1. How can you simplify expressions with multiple square roots?
  2. What is the rationalization technique for fractions with square roots in the denominator?
  3. How do you add fractions with square roots in the numerator?
  4. What happens if you square both sides of an expression involving square roots?
  5. How do you calculate the value of an expression involving square roots?

Tip: When dealing with expressions involving square roots, always look for a common denominator if adding or subtracting fractions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Roots
Fractions

Formulas

Simplifying square roots
Combining fractions with common denominators

Theorems

Basic properties of square roots
Rationalizing expressions

Suitable Grade Level

Grades 8-10