Math Problem Statement

\sqrt{\dfrac{36}{169}} =

Solution

The expression you provided is:

36169\sqrt{\dfrac{36}{169}}

To solve this:

  1. Take the square root of the numerator (36) and the square root of the denominator (169) separately.

36=6and169=13\sqrt{36} = 6 \quad \text{and} \quad \sqrt{169} = 13

  1. Therefore:

36169=613\sqrt{\dfrac{36}{169}} = \dfrac{6}{13}

The final answer is:

613\dfrac{6}{13}

Would you like further details or have any questions?

Here are some related questions to explore:

  1. What is the square root of other fractions, such as 4981\sqrt{\dfrac{49}{81}}?
  2. How do you simplify square roots of non-perfect squares?
  3. What are the properties of square roots of negative numbers (complex numbers)?
  4. How do square roots relate to exponents?
  5. How would you solve 25100\sqrt{\dfrac{25}{100}}?

Tip: When simplifying square roots of fractions, always simplify the square root of the numerator and denominator separately if possible!

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Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Fractions

Formulas

√(a/b) = √a / √b

Theorems

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Suitable Grade Level

Grades 6-8