Question

What is the square root of 1800 in simplest radical form?

Answer 1

Hint: For solving this type of questions you should know about the radical form of any value for calculate the square root or you can also calculate cube root also by this, and in this you divide provided number till last value will be 1 or we can say that we have to divide it completely and then we make pairs for some digits and take them outside the root and now multiply them and calculate the final answer.

Complete step by step answer:
In the question it is given that we have to find the square root of 1800 in simplest radical form.
According to the questions if they are asking for the understood of any form or order then if you use simplest radical form then it just means simplifying a radical so that there no more square roots cube roots, \[{{4}^{th}}\] roots etc left to find in that. It also means to remove any radicals in the denominator of a fraction of any type. We can find the \[{{n}^{th}}\] root of any digit by it, if that is a complete square of \[{{n}^{th}}\] powered digit.
So, for calculating that we have to find all largest perfect squares step by step.
For this we can do it as:
\[\begin{align}
  & 2\left| \!{\underline {\,
  1800 \,}} \right. \\
 & 2\left| \!{\underline {\,
  900 \,}} \right. \\
 & 2\left| \!{\underline {\,
  450 \,}} \right. \\
 & 5\left| \!{\underline {\,
  225 \,}} \right. \\
 & 5\left| \!{\underline {\,
  45 \,}} \right. \\
 & 3\left| \!{\underline {\,
  9 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & 1 \\
\end{align}\]
So, we can also write \[\sqrt{1800}\] as
\[\sqrt{1800}=\sqrt{2\times 2\times 2\times 5\times 5\times 3\times 3}\]
We have to make pair and taking them outside the under root
\[\begin{align}
  & \sqrt{1800}=2\times 5\times 3\sqrt{2} \\
 & \sqrt{1800}=30\sqrt{2} \\
\end{align}\]

So, the square root of \[\sqrt{1800}\] is \[30\sqrt{2}\]. And we found it by the radical form.

Note: During the solution of this question we have to be careful during the dividing the values and we have made maximum possible pairs, which can become in the dividation. Because these help to make the under root very much easier.