Question

23) The integral part of (√2 +1)^6 is​

Answer 1

Answer:

According to the question, the correct answer is 99.

Step-by-step explanation:

( √2 +1 )⁶

= ⁶c₀(√2)⁶ + ⁶c₁(√2)⁵ + ⁶c₂(√2)⁴ + ⁶c₃(√2)³ + ⁶c₄(√2)² + ⁶c₅(√2) + ⁶c₆

= (√2)⁶ + 6(√2)⁵ + 15(√2)⁴ + 20(√2)³ + 15(√2)² + 6(√2) + 1

= 8 + 24√2 + 60 + 40√2 + 30+ 6√2 + 1

= ( 8 + 60 + 30 + 1) + √2( 24 + 40+ 6 )

= 99 + 70√2

So, the integral part of (√2 +1)^6 is 99.