Question

How do you divide radical by whole numbers? \[\]

Answer 1

Hint: We recall the meaning of radical and the definition of whole numbers. We recall that radical is always in the form of $\sqrt[p]{n}$ which means ${{p}^{th}}$ root of $n$. If we can simplify $\sqrt[p]{n}$ to a whole number or an integer we can divide the radical by whole number using decimal division process otherwise we have to find $\sqrt[p]{n}$ using a scientific calculator and then divide by the whole number .\[\]


Complete step by step answer:
We know that radical is ${{p}^{th}}$ root of an number $n$ expressed with radical sign ‘$\sqrt{{}}$’ and written as $\sqrt[p]{n}$. If $p=2$ we call the radical square root and write as $\sqrt{n}$. If $p=3$ we call it cube root and write it as $\sqrt[3]{n}$ and we follow this process for $p\ge 4$. If $p$ is even then $n$ cannot be negative for the root to be real .
We know that whole numbers are non-negative integers which mean number 0 and the natural numbers $1,2,3,...$. We know that we cannot divide by 0. So we can use other whole numbers to divide. \[\]
We have now two possible cases either the result of the radical is an integer or an irrational number. If it is in integer we can divide it by using the decimal division method. For example the radical $\sqrt{16}$ simplifies to $\sqrt{16}=4$. We can divide it by any whole number say $10$to have
\[4\div 10=0.4\]
If the radical cannot be simplified to integer for example $\sqrt{5}$ then we have to use a calculator to find the decimal value approximately. We use a calculator to find approximate $\sqrt{5}\approx 2.2360$. We can divide by 10 to have;
$\Rightarrow$ \[\sqrt{5}\div 10\approx 2.2350\div 10=2.2350\]

Note:
 We note that all radicals which cannot be simplified to a rational number are called irrational radicals for example $\sqrt{5}$ and radicals that can be simplified to rational numbers are called rational numbers. The radicals as square roots of a perfect square and the cube root of a perfect cube are radical rationales. Similarly, the ${{p}^{th}}$ root of $n$ raised to the power multiple of $p$ is radical rational.