https://file.aiquickdraw.com/mathbot/file/17267599883889rzq0hgu.jpg

It looks like you've uploaded a mathematical expression. Let's solve and simplify it.

The expression in the image is:
\[
\sqrt{\frac{324}{729}} + \left(1 - \sqrt{\frac{169}{676}}\right) + \frac{1}{2}
\]

We'll break it down step-by-step:

1. **Square root of a fraction**: The square root of a fraction can be calculated by taking the square root of the numerator and the denominator separately.
   \[
   \sqrt{\frac{324}{729}} = \frac{\sqrt{324}}{\sqrt{729}} = \frac{18}{27} = \frac{2}{3}
   \]
   
2. **Square root in subtraction**:
   \[
   1 - \sqrt{\frac{169}{676}} = 1 - \frac{\sqrt{169}}{\sqrt{676}} = 1 - \frac{13}{26} = 1 - \frac{1}{2} = \frac{1}{2}
   \]
   
3. **Adding the fractions and constants**:
   \[
   \frac{2}{3} + \frac{1}{2} + \frac{1}{2}
   \]

   To add these, we need a common denominator. The common denominator for 3 and 2 is 6:
   \[
   \frac{4}{6} + \frac{3}{6} + \frac{3}{6} = \frac{10}{6} = \frac{5}{3}
   \]

Thus, the value of the entire expression is \(\frac{5}{3}\).

Would you like more details on any of these steps or do you have another question? Here are a few things you might find interesting:
1. Why do we need to find a common denominator to add fractions?
2. What are other examples where subtracting square roots might be used in expressions?
3. How to simplify square roots of larger numbers?
4. What techniques can be used to find the square root of a non-perfect square without a calculator?
5. How would this expression change if the operations between the numbers were different (e.g., multiplication instead of addition)?

Tip: Remember, when dealing with square roots of fractions, simplify within the square root before taking the square root if possible—it often makes the arithmetic easier!

Solve the expression: (√324 / √729) + (1 - √169 / √676) + 1/2

Learn how to simplify and solve the mathematical expression involving square roots and fractions: (√324 / √729) + (1 - √169 / √676) + 1/2. This problem covers concepts such as square roots, fraction simplification, and arithmetic operations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation