If√10=3.162 Then Find the Value of 1/√10


Question: If √10 = 3.162 then find the value of 1/√10

The given problem is based on the rationalization of irrational numbers.

Answer: The value 1/√10 is 0.3162. 

Let's understand the process of rationalization in detail.

Explanation:

Rationalization is the process of eliminating a radical or imaginary number from the denominator or numerator of an algebraic fraction.

Rationalization removes the radicals in a fraction so that the denominator or numerator only contains a rational number. Thus, the denominator needs to be rationalized to make the expression become a rational number.

1/√10 = (1/√10) × 1 = (1/√10) × (√10/√10) = ( 1 × √10 ) / (√10 × √10) = √10 / 10

⇒ 1/√10 =  √10 / 10 

Given that √10 = 3.162

⇒ 1/√10 =  √10 / 10 = 3.162 / 10 = 0.3162.

Therefore, 1/√10 =  √10 / 10 = 0.3162

So, if √10=3.162 then the value of 1/√10 is 0.3162