Question

Given that $\sqrt {1225} = 35$ , find the value of $\sqrt {12.25} + \sqrt {0.1225} + \sqrt {0.001225} .$

A. $0.3885$

B. $388.5$

C. $38.85$

D. $3.885$

Answer 1

Hint- We have to use the given square root of \[1225\] to solve this question, so at first we will write the equation in fractional form further we will take the square root of denominator and numerator and at last we will simply add all the terms.

Complete step-by-step answer:
Given that $\sqrt {1225} = 35$
We have to find the value of $\sqrt {12.25} + \sqrt {0.1225} + \sqrt {0.001225} .$
Here we will first convert the term above into fractional form by removing decimal, so we have

\[
  \sqrt {12.25} = \sqrt {1225/100} \\
  \sqrt {0.1225} = \sqrt {1225/10000} \\
  \sqrt {0.001225} = \sqrt {1225/1000000} \\
\]
Now we're going to take square denominator root as well as numerator separately, so we get
\[\sqrt {1225/100} + \sqrt {1225/10000} + \sqrt {1225/1000000} \] \[ - (1)\]
As we know that
\[\begin{array}{*{20}{l}}
  {\sqrt {100} {\text{ }} = {\text{ }}10} \\
  \; \\
  {\sqrt {10000} = {\text{ }}100} \\
  \; \\
  {\sqrt {1000000} {\text{ }} = {\text{ }}1000}
\end{array}\]
And given $\sqrt {1225} = 35$
Substitute all the square root values in equation 1, we will get
\[35/10 + 35/100 + 35/1000\]
Further dividing all the term separately we get
\[3.5 + {\text{ }}0.35{\text{ }} + {\text{ }}0.035\]
Now , simply we will add all the term
\[3.885\]

Hence the correct answer is option D.

Note-Each non-negative real number$X$ has a unique non-negative square root, called the principal square root, denoted by$\sqrt X $, where the symbol $\sqrt {} $ is called the radical sign or radix.