## Surds and Indices

#### Surds and Indices

1. If m = 7 - 4√3, then (√m + 1/√m) = ?

1. 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

1. (100)0 is equivalent to :

1. 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.

1. If √2n = 64 , what will be the value of n?

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.

1. The value of 6a3 b3 c2 ÷ 2ab2 c is :

1. 6a3 b3 c2 ÷ 2ab2c

 = 6a3b3c2 2ab2c

##### Correct Option: B

6a3 b3 c2 ÷ 2ab2c

 = 6a3b3c2 2ab2c

= 3a3 - 1 b3 - 2 c2 - 1 = 3a2bc

1. If m and n are natural numbers, the m√n

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

##### Correct Option: B

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