Question

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

Answer 1

Hint: Write $\sqrt {45} = \sqrt {9 \times 5} ,\sqrt {605} = \sqrt {121 \times 5} ,\sqrt {245} = \sqrt {49 \times 5} $ in the expression given $\sqrt {45} + \sqrt {605} - \sqrt {245} $ and then find the answer.

Complete step-by-step answer:
According to the question it is given that-
$\sqrt 5 = 2.236$.
The expression is- $\sqrt {45} + \sqrt {605} - \sqrt {245} \to (1)$
Putting $\sqrt {45} = \sqrt {9 \times 5} ,\sqrt {605} = \sqrt {121 \times 5} ,\sqrt {245} = \sqrt {49 \times 5} $ in equation (1)-
$
  \sqrt {45} + \sqrt {605} - \sqrt {245} \\
   = \sqrt {9 \times 5} + \sqrt {121 \times 5} - \sqrt {49 \times 5} \\
   = 3\sqrt 5 + 11\sqrt 5 - 7\sqrt 5 \\
 $
Now, put $\sqrt 5 = 2.236$ in the above equation, we get-
$
   \Rightarrow 3 \times 2.236 + 11 \times 2.236 - 7 \times 2.236 \\
   = 6.708 + 24.596 - 15.652 \\
   = 31.304 - 15.652 \\
   = 15.652 \\
$
Hence, the correct option is A. 15.652.

Note: Whenever such types of questions appear then write down the expression given in the question whose value is to be found out. Since, it is given that $\sqrt 5 = 2.236$, so try to express each term in the form of $\sqrt 5 $ to simplify it and then solve to get the answer.