Math Problem Statement

Simplify the square root expression \(\sqrt{25x^2y^2}\).

Solution

The expression you provided is:

25x2y2\sqrt{25x^2y^2}

To simplify this expression, we can break it down as follows:

25x2y2=25x2y2\sqrt{25x^2y^2} = \sqrt{25} \cdot \sqrt{x^2} \cdot \sqrt{y^2}

Now, simplify each part:

  1. 25=5\sqrt{25} = 5
  2. x2=x\sqrt{x^2} = x (assuming x0x \geq 0)
  3. y2=y\sqrt{y^2} = y (assuming y0y \geq 0)

So, the simplified form of the expression is:

5xy5xy

Would you like more details on this process or have any further questions?


Here are five related questions to consider:

  1. How would the simplification change if xx or yy could be negative?
  2. What if the expression under the square root was 49x4y4\sqrt{49x^4y^4}?
  3. How do you simplify x4+y4\sqrt{x^4 + y^4}?
  4. Can you apply the same process to simplify 100x6y2\sqrt{100x^6y^2}?
  5. What are the rules for simplifying square roots of products and quotients?

Tip: Always consider the domain (possible values) of the variables when simplifying expressions involving square roots, as this can affect the final form.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Square Roots

Formulas

\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)
\(\sqrt{x^2} = x\) if \(x \geq 0\)
\(\sqrt{y^2} = y\) if \(y \geq 0\)

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 8-10