Square Root Of 4/9: Simple Explanation & Calculation
Table of Contents :
Understanding the square root of a fraction can be quite straightforward once you break it down into simpler parts. Today, we’ll explore the square root of ( \frac{4}{9} ) in detail, using simple explanations and calculations. 🌟
What is a Square Root?
Before diving into the specific calculation, let’s clarify what a square root is. The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 9 is 3, since ( 3 \times 3 = 9 ). Similarly, the square root of a fraction can be calculated using the same principle.
Basic Formula
The square root of a fraction ( \frac{a}{b} ) can be calculated with the formula:
[ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} ]
Using this formula, we can find the square root of ( \frac{4}{9} ).
Calculating the Square Root of ( \frac{4}{9} )
Now let's apply our formula step-by-step:
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Identify the Numerator and Denominator:
- Numerator ( a = 4 )
- Denominator ( b = 9 )
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Calculate the Square Roots:
- ( \sqrt{4} = 2 ) (because ( 2 \times 2 = 4 ))
- ( \sqrt{9} = 3 ) (because ( 3 \times 3 = 9 ))
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Put It All Together: [ \sqrt{\frac{4}{9}} = \frac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3} ]
So, the square root of ( \frac{4}{9} ) is ( \frac{2}{3} ). 🎉
Verification of the Result
It’s always a good practice to verify our calculations. To confirm that our answer is correct, we can square ( \frac{2}{3} ) and check if we return to ( \frac{4}{9} ):
[ \left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9} ]
Since we have verified that squaring ( \frac{2}{3} ) indeed results in ( \frac{4}{9} ), our calculation is correct! ✅
Key Takeaways
- The square root of a fraction can be simplified using the square root of its numerator and denominator.
- The calculation of ( \sqrt{\frac{4}{9}} ) yields ( \frac{2}{3} ).
- Always verify your results by squaring your answer to ensure accuracy.
Understanding how to work with square roots, especially for fractions, is an essential skill in mathematics. With practice, you’ll find this process becomes intuitive. Keep exploring, and you’ll master these calculations in no time! 📚✨