Question

Given $ \sqrt{5}=2.236 $ the value of $ \sqrt{45}+\sqrt{605}-\sqrt{245} $ correct to 3 decimal places is
A. $ 15.652 $
B. $ 11.180 $
C. $ 18.652 $
D. $ 16.652 $

Answer 1

Hint: To solve this question first of all we simplify the given expression. We have been given the value of $ \sqrt{5}=2.236 $ , so we will try to factorize the given expression in the form of $ \sqrt{5} $ . We will use the basic square roots of the numbers to solve this question. Then substitute the value and solve further to get the desired answer.

Complete step by step answer:
We have been given that $ \sqrt{5}=2.236 $ .
We have to find the value of $ \sqrt{45}+\sqrt{605}-\sqrt{245} $ .
Now, we know that we can write $ \sqrt{45}=\sqrt{5\times 9} $ and $ \sqrt{9}=3 $ so we get $ \sqrt{45}=3\sqrt{5} $
Similarly we can write $ \sqrt{605}=\sqrt{121\times 5} $ and $ \sqrt{121}=11 $ so we get $ \sqrt{605}=11\sqrt{5} $
Now, we can write $ \sqrt{245}=\sqrt{49\times 5} $ and $ \sqrt{49}=7 $ so we get $ \sqrt{245}=7\sqrt{5} $
Now, substituting the values in the given expression we get
 $ \Rightarrow 3\sqrt{5}+11\sqrt{5}-7\sqrt{5} $
Now, solving the above equation we get
 $ \begin{align}
  & \Rightarrow 14\sqrt{5}-7\sqrt{5} \\
 & \Rightarrow 7\sqrt{5} \\
\end{align} $
Now, we have given in the question $ \sqrt{5}=2.236 $
Substitute the value in the obtained equation we get
 $ \begin{align}
  & \Rightarrow 7\times 2.236 \\
 & \Rightarrow 15.652 \\
\end{align} $
Hence we get $ \sqrt{45}+\sqrt{605}-\sqrt{245}=15.652 $
We have asked in the question that we have to find the value correct to 3 decimal places.
So, the correct answer is option A.

Note:
The key concept to solve this question is the conversion of the given expression in $ \sqrt{5} $ form because the given numbers are not perfect squares so we can’t find the square root of the given numbers. Students must know the square root of the basic numbers to solve these types of questions.