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How to Rationalize the Denominator 🧮✨

Struggling with rationalization? In this video, I’ll show you an easy step-by-step method to remove square roots from the denominator and simplify fractions! 🚀

Step 1: Understand Rationalization
📌 Rationalization is the process of eliminating square roots (or surds) from the denominator of a fraction.
📌 This is done by multiplying the numerator and denominator by a suitable value.

Step 2: Rationalizing Simple Surds
🔹 Example 1: Rationalizing 1/√5
✔ Multiply by √5/√5
✔ (1 × √5) / (√5 × √5)
✔ = √5 / 5 ✅

🔹 Example 2: Rationalizing 3/√7
✔ Multiply by √7/√7
✔ (3 × √7) / (√7 × √7)
✔ = 3√7 / 7 ✅

Step 3: Rationalizing Binomial Denominators
When the denominator is in the form a + √b, multiply by its conjugate a - √b to remove the square root.

🔹 Example: Rationalizing 1 / (3 + √2)
✔ Multiply by (3 - √2) / (3 - √2)
✔ Apply the difference of squares formula:
✔ (1 × (3 - √2)) / ((3 + √2)(3 - √2))
✔ = (3 - √2) / (9 - 2)
✔ = (3 - √2) / 7 ✅

Step 4: Final Tips
🔹 Always multiply by a suitable value to simplify the denominator.
🔹 When rationalizing binomial denominators, use the conjugate to eliminate the square root.
🔹 Keep practicing to get faster at these steps!

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