Question

How do you simplify $\sqrt {468}?$

Answer 1

Hint: The square root of “n” is a quantity “q” which will equal “n” when multiplied by itself. To simplify the given root check whether it is a perfect square or not. If not a perfect square then definitely its square root will be irrational so better simplify it to a smaller radical also called “to simplify a surd” rather than simplifying it to decimal places because irrational numbers have infinite number of decimals so better not deal with it.Root of a perfect square is given as, ${a^2} = \sqrt {a \times a} $

Complete step by step answer:
We will first define, evaluate, and then simplify $\sqrt {468} $. We begin with the definition and then answer some common questions about the square root of $468$. Then, we will simplify $\sqrt {468} $.In mathematical form, the square root of $468$ is written as $\sqrt {468} $ with the radical sign. The $\sqrt {468} $ is a quantity $(n)$ that will equal $468$ when multiplied by itself.
$n \times n = {n^2} = 468$

Is $468$ a perfect square? When the square root of $468$ is equal to the whole number, $468$ is a perfect square. The square root of $468$ is not an entire number, as we have calculated below. So it is not a perfect square. We will simplify it to smaller radical,
We can write $\sqrt {468} $ as
$\sqrt {468} = \sqrt {6 \times 6 \times 13} \\
\therefore\sqrt {468}= 6\sqrt {13} $

Therefore the simplified form of $\sqrt {468} \;{\text{is}}\;6\sqrt {13}$

Note: Know that negative times negative are identical to positive times. Thus, not only does the square root of $468$ have the positive answer we explained above, but also the negative counterpart.If you want the result in decimals then with the use of calculator find the approximate value of $6\sqrt {13} $ or rather you can go with long division method.