Answer

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**Hint:**First of all solve the expression given in the question by multiplying and adding the decimal numbers. After reducing the given expression to a number then find the square root and then compare the answer with the options given in the above problem.

__Complete step-by-step answer__:The expression that we have to find the square root of is given in the above problem as:

$0.09+2\times 0.21+0.49$

Multiplying 2 by 0.21 in the above expression we get,

$0.09+0.42+0.49$

Adding all the decimal numbers given in the above expression we get,

$\begin{align}

& \text{ }0.09 \\

& +0.42 \\

& \dfrac{+0.49}{1.00} \\

\end{align}$

The result of the above addition is 1 so taking square root of 1 we get,

$\sqrt{1}$

We can also write 1 in the square root as ${{\left( 1 \right)}^{2}}$ in the above.

$\sqrt{{{\left( 1 \right)}^{2}}}$

$=1$

From the above solutions, we have found the square root of the given expression as 1.

Now, on comparing the answer that we have got which is 1 from the options given in the above problem the correct option is (c).

**Hence, the correct option is (c).**

**Note**:The plausible mistakes that could happen in solving the above problem is that on multiplication of 2 by 0.21 you might miss out in writing the decimal point like on multiplying 2 by 0.21 you might write the answer as 4.2 or 0.0042. The other mistake that could happen is in the addition of the decimals that we have shown in the above solution as:

$0.09+0.42+0.49$

In the above addition, if you have not stacked the decimal numbers correctly then you will end up getting the wrong answer. This is the correct stacking that we have shown above.

$\begin{align}

& \text{ }0.09 \\

& +0.42 \\

& \dfrac{+0.49}{1.00} \\

\end{align}$

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