Question

If $ \sqrt {10} = 3.162 $ , then the value of $ \dfrac{1}{{\sqrt {10} }} $ is
A. 0.3162
B. 3.162
C. 31.62
D. 316.2

Answer 1

Hint: To find the value of $ \dfrac{1}{{\sqrt {10} }} $ , we have to first rationalize its denominator by multiplying and dividing by $ \sqrt {10} $ . Rationalizing a denominator means getting rid of any square roots or cube roots by multiplying and dividing the given number by its denominator’s conjugate. The conjugate should be in such a form that when it is multiplied to the given denominator, it must become an integer. So here we have a square root in the denominator, so we have to multiply it with another square root to get rid of the root.

Complete step-by-step answer:
We are given the value of $ \sqrt {10} $ and we have to find the value of $ \dfrac{1}{{\sqrt {10} }} $ .
First we are rationalizing $ \dfrac{1}{{\sqrt {10} }} $ by multiplying and dividing it with $ \sqrt {10} $
 This gives
 $ \Rightarrow \dfrac{1}{{\sqrt {10} }} \times \dfrac{{\sqrt {10} }}{{\sqrt {10} }} $ which is equal to $ \dfrac{{\sqrt {10} }}{{10}} $
We already know the value of $ \sqrt {10} = 3.162 $ , so we are substituting it in the above expression.
 $ \Rightarrow \dfrac{{3.162}}{{10}} $
In 3.162, we have three more digits after the decimal point; this means that 3162 divided by a thousand gives 3.162.
 $ \Rightarrow \dfrac{{\left( {\dfrac{{3162}}{{1000}}} \right)}}{{10}} $
Sending 1000 to the denominator, we get
 $ \Rightarrow \dfrac{{3162}}{{10000}} $
As we can see the denominator is ten thousand with 4 zeros, so the result will have four digits after the decimal point.
  $ \Rightarrow \dfrac{{3162}}{{10000}} = 0.3162 $
Therefore, the value of $ \dfrac{1}{{\sqrt {10} }} $ is $ 0.3162 $
So, the correct answer is “Option A”.

Note: Whenever we send a variable or a number inside a square root, the number becomes its square such as 3 becomes 9, 5 becomes 25 etc; whenever we send a variable or a number inside a cube root, the number becomes its cube such as 3 becomes 27, 5 becomes 125 etc. And to get rid of a square root, we need a product of two similar numbers. Here we already had a 10 and we have multiplied it with one more 10.