Question

What is the square root of $63$ in simplest radical form?

Answer 1

Hint: Here we have to calculate the square root of the $63$ in simplest radical form. Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, etc left to find. Now the given number is a real number.

Complete step by step solution:
The given number is $63$. Since we can see the given number is not a perfect square. A perfect square is a number which is generated by multiplying two equal integers by each other. For example, the number $9$ is a perfect square because it can be expressed as a product of two equal integers: $9=3\times 3$.
We have to calculate the square root of $63$, mathematically we can write it as:
$\Rightarrow \sqrt{63}$
Since we can write $63$ in the product of prime factors as:
$\Rightarrow 63=3\cdot 3\cdot 7$
Now applying under root or square root on both side of expression, then we get
$\Rightarrow \sqrt{63}=\sqrt{3\cdot 3\cdot 7}=\sqrt{9\cdot 7}$
Since we have discussed above about the perfect square, here number $9$ is a perfect square and can be written in the product of two same numbers which is $3$. So it comes out of the square root, then we get
$\Rightarrow \sqrt{63}=3\sqrt{7}$
Hence we get the required square root in the simplest form.

Note: Whenever we have these types of questions we should know about the radical expression and the method to convert the numbers to the radical expression. And we should know the perfect square numbers so that whenever we write any number in the product of prime factors we can easily remove them from under root.