Question

How do you rewrite in simple radical form: \[\sqrt{20}\] ?

Answer 1

Hint: These are very simple problems of algebra and can easily be solved by following some easy steps. First of all we need to understand what the simplest radical form means. The simplest radical form means, the form which cannot be further square rooted. The general form of square root of two numbers is defined as,
\[\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}\] . The conditions for this equation is \[a,b\ge 0\] . We can further reduce the given problem by writing it in general form and trying to express it in terms of some perfect squares.

Complete step by step answer:
Now, we start off the solution by writing the number $20$ , into some multiplication of a perfect square number (if possible) and some other number (if possible). We see that we can easily try and write it in that form, that is,
We can write 20 as \[\sqrt{20}=\sqrt{4\cdot 5}=\sqrt{4}\cdot \sqrt{5}\] . Now from this deduction, we can very easily observe that \[5\] is not a perfect square, and we can also see that \[4\] is a perfect square. Hence we can further reduce \[4\] to its simplest form. We can write,
\[\sqrt{4}=\sqrt{2\times 2}\] , writing it on the square form, we write,
 \[\sqrt{{{2}^{2}}}\]. This, we can easily write as \[2\] . Now we can replace this in our original equation as,
\[\sqrt{20}=2\cdot \sqrt{5}\] . Thus the simplest radical form of \[\sqrt{20}\] can be written down as,
\[\sqrt{20}=2\sqrt{5}\] .

Note:
For these types of questions, we must always remember the exact definition of simplest radical form. We must also keep in mind of the general equation that represents the simplest radical form. For these problems, we also have to very intelligently figure out how we should be able to express the number given inside the square root into a square form or its closest square form.