Question

If $\sqrt{3}=1.732$ then the approximate value of $\dfrac{1}{\sqrt{3}}$ is
(A)$0.617$
(B)$0.313$
(C)$0.577$
(D)$0.173$

Answer 1

Hint: For answering this question that is for finding the value of $\dfrac{1}{\sqrt{3}}$ using the value $\sqrt{3}=1.732$ . We will multiply and divide it with $\sqrt{3}$ . And simplify it and substitute the value of $\sqrt{3}$ as $1.732$ in it and simplify it and find the value of $\dfrac{1}{\sqrt{3}}$ .

Complete step by step answer:
Here in this question it is given as $\sqrt{3}=1.732$ we need to find the value of $\dfrac{1}{\sqrt{3}}$. For this we will multiply and divide it by $\sqrt{3}$ after that we will have $\dfrac{1}{\sqrt{3}}\times \dfrac{\sqrt{3}}{\sqrt{3}}$ .
After simplifying this we will have $\dfrac{\sqrt{3}}{3}$ .
Since we know the value of $\sqrt{3}=1.732$ we will substitute it here $\dfrac{1.732}{3}$ .
After further simplifying we will have $0.577$ .
So we end up with a conclusion that when $\sqrt{3}=1.732$ the approximate value of $\dfrac{1}{\sqrt{3}}$ is $0.577$.

So, the correct answer is “Option C”.

Note: We can also solve this question in another way that is without multiplying and dividing it with $\sqrt{3}$ . We will directly substitute the value of $\sqrt{3}$in$\dfrac{1}{\sqrt{3}}$ after that we will have $\dfrac{1}{1.732}$. After multiplying and dividing it with 1000 we will have $\dfrac{1}{1.732}\times \dfrac{1000}{1000}=\dfrac{1000}{1732}$. After simplifying this by taking 4 as common in both numerator and denominator we will have $\dfrac{1000}{1732}=\dfrac{\left( 4 \right)250}{\left( 4 \right)433}$. After cancelling the 4 in both numerator and denominator we will have $\dfrac{\left( 4 \right)250}{\left( 4 \right)433}=\dfrac{250}{433}$. After performing the further calculations we will have $0.577$. So we have the same answer in both the cases, that is when $\sqrt{3}=1.732$ the approximate value of $\dfrac{1}{\sqrt{3}}$ is$0.577$ . Similarly we can also find the value of any other required numbers.