Class 10 - Ex -1.2 SOLVED BY PREM SIR

Irrational Numbers - Class 10
PREM KA

📘 Class 10 Maths – Prove these numbers are Irrational

✍️ Solved by: Prem Sir
📍 Address: B312/6, Indra Enclave Phase 1, Kirari
📞 Contact: 6200409895

Q1. सिद्ध कीजिए कि √5 एक अपरिमेय संख्या है।
Prove that √5 is an irrational number.
Maan lo √5 ek rational number hai → √5 = a/b (co-prime, b ≠ 0)
Squaring: 5 = a²/b² ⇒ a² = 5b²
To a bhi 5 se divisible ⇒ a = 5k
Fir b bhi 5 se divisible ho gaya ⇒ contradiction ⚠️
✅ So √5 is irrational.
Q2. सिद्ध कीजिए कि 3 + 2√5 एक अपरिमेय संख्या है।
Prove that 3 + 2√5 is an irrational number.
Assume 3 + 2√5 rational hai
⇒ 2√5 = rational - 3 ⇒ √5 = rational/2
Par √5 irrational hai ❌ contradiction
✅ So 3 + 2√5 is irrational
Q3(i). सिद्ध कीजिए कि 1/√2 एक अपरिमेय संख्या है।
Prove that 1/√2 is an irrational number.
√2 irrational hai, aur rational ÷ irrational = irrational
✅ So 1/√2 is irrational
Q3(ii). सिद्ध कीजिए कि 7√5 एक अपरिमेय संख्या है।
Prove that 7√5 is an irrational number.
√5 irrational hai, aur rational × irrational = irrational
✅ So 7√5 is irrational
Q3(iii). सिद्ध कीजिए कि 6 + √2 एक अपरिमेय संख्या है।
Prove that 6 + √2 is an irrational number.
Rational (6) + Irrational (√2) = Irrational
✅ So 6 + √2 is irrational

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