Given that ,
m = 7 - 4√3
Then I/m = 1/7 - 4√3......................(1)

Now multiply and divide with 7 + 4√3 in Eq. (1)
We will get,
1/m = ( 1/7 - 4√3 ) x ( 7 + 4√3 / 7 + 4√3)
⇒1/m = ( 7 + 4√3 )/ ( 7 - 4√3 ) x ( 7 + 4√3

Correct Option: C

Given that ,
m = 7 - 4√3
Then I/m = 1/7 - 4√3......................(1)

Now multiply and divide with 7 + 4√3 in Eq. (1)
We will get,
1/m = ( 1/7 - 4√3 ) x ( 7 + 4√3 / 7 + 4√3)
⇒1/m = ( 7 + 4√3 )/ ( 7 - 4√3 ) x ( 7 + 4√3
⇒1/m = ( 7 + 4√3 ) / ( 7² - ( 4√3)² )
⇒1/m = ( 7 + 4√3 ) / ( 49 - 4 x 4 x 3 )
⇒1/m = ( 7 + 4√3 ) /49 - 48
⇒1/m = ( 7 + 4√3 ) / 1
⇒1/m = 7 + 4√3
∴ m + 1/m = 14
⇒ ( m + 1/m ) + 2 = 14 + 2 = 16
∴ (√m + 1/√m)² = ( m + 1/m )+ 2
⇒ (√m + 1/√m)² = 16
⇒ (√m + 1/√m)² = 4²
⇒ (√m + 1/√m) = 4

If any given number (suppose x) is a rational number other than zero, then x⁰ = 1.

Correct Option: C

If any given number (suppose x) is a rational number other than zero, then x⁰ = 1.

√2ⁿ = 64 ⇒ 2ⁿ = (64)²
⇒ 2ⁿ = (2 × 2 × 2 × 2 × 2 × 2)²
⇒ 2ⁿ = (26)² ⇒ 2ⁿ

Correct Option: C

√2ⁿ = 64 ⇒ 2ⁿ = (64)²
⇒ 2ⁿ = (2 × 2 × 2 × 2 × 2 × 2)²
⇒ 2ⁿ = (26)² ⇒ 2ⁿ = 26 × 2 = 212
⇒ n = 12.

6a³ b³ c² ÷ 2ab²c

Correct Option: B

6a³ b³ c² ÷ 2ab²c

If m and n are natural numbers, then m√n is irrational unless n is m^th power of an integer.

Correct Option: B

If m and n are natural numbers, then m√n is irrational unless n is m^th power of an integer.