Three Surds in the Denominator — Eliminated One by One With Pure Elegance | Math Olympiad

Описание: Math Olympiad Challenge — Three Radicals in the Denominator!

10/(√5 + √3 + √8) = ?

When most students see three different surds
sitting together in a denominator, they freeze.

How do you rationalize THREE radicals at once?
You can't just multiply by one conjugate —
can you?


Watch the denominator collapse to 2√15 —
a single radical — after a stunning
difference of squares.

Then one final rationalization wipes out √15
completely and leaves a clean, beautiful
three-term answer:

(5√3 + 3√5 - 2√30) / 3

Two rationalizations. Three terms. One elegant answer.

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🧠 What You'll Learn:
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✔️ Why simplifying √8 = 2√2 is the crucial first step
✔️ How to group three radicals into two parts for conjugate
✔️ How (√5+√3)²-(2√2)² = 2√15 via difference of squares
✔️ How the denominator collapses from three surds to one
✔️ How √15·√5 = 5√3 and √15·√3 = 3√5 simplify perfectly
✔️ Why the final answer (5√3+3√5-2√30)/3 is fully simplified
✔️ A two-stage rationalization strategy reusable for ANY
three-surd denominator


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📌 Try It Yourself First!
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Pause before the solution — can you
figure out which two terms to group
together for the first conjugate?
That grouping decision is the entire key!
Drop your approach in the comments below!
Did you get (5√3+3√5-2√30)/3? 👇

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