Question

What is the square root of 1.8?

Answer 1

Hint: We are asked to find the square root of the given number. To find this, first we can simplify it by multiplying and dividing suitable numbers inside the root and then take the factors of the number inside the root. Then we take the perfect squares outside the root and obtain the simplified version of the number. To find the exact value, one can use the manual method or one can use a calculator to find the root.

Complete step by step answer:
The number for which we need to find the square root, given in the question is 1.8, so we are asked to find the value of $\sqrt{1.8}$ . We can simplify the value inside the square root by multiplying and dividing suitably numbers. Since we have a decimal we would like to convert it into a fraction by multiplying and dividing 10. Doing so, we get,
$\begin{align}
  & \sqrt{1.8}=\sqrt{\dfrac{1.8\times 10}{10}} \\
 & \sqrt{1.8}=\sqrt{\dfrac{18}{10}} \\
\end{align}$
Next, we can write 18 in terms of its factors as,
$\begin{align}
  & 18=3\times 3\times 2 \\
 & 18={{3}^{2}}\times 2 \\
\end{align}$
Hence, we can take 3 outside the square root and now we are left with,
$\begin{align}
  & \sqrt{\dfrac{18}{10}}=\sqrt{\dfrac{{{3}^{2}}\times 2}{10}} \\
 & \sqrt{\dfrac{18}{10}}=3\sqrt{\dfrac{2}{10}} \\
 & \sqrt{\dfrac{18}{10}}=\dfrac{3}{\sqrt{5}} \\
\end{align}$
Therefore, we have obtained the simplified result for the given decimal number as $\dfrac{3}{\sqrt{5}}$. If we want to find the answer in decimal, then using a calculator we can find the exact value. It turns out to be 1.3416.

Note: Another way to directly evaluate the result is to enter 1.8 into the calculator and find its square root. By doing so we arrive at the same result, 1.3416. Also, we have only considered the positive value here, since the square of a negative number is also positive sometimes even the negative root has to be considered. Hence the answer ideally will be $\pm 1.3416$ . Unless mentioned we only take the positive root as the answer.