Question

What is the simplest radical form of \[\sqrt{169}\]?

Answer 1

Hint: In this problem, we have to find the simplest radical form of \[\sqrt{169}\]. We should know that every positive number has two square roots, one positive and one negative. If we only want the positive square root of a positive number then we use a radical sign, \[\sqrt{m}\], which denotes the positive square root of m. Here we have a perfect square number for which we can find the simplest radical form.

Complete step by step solution:
We know that the given square root is,
 \[\sqrt{169}\]
Here we have to find its simplest radical form.
We know that 169 is the 13 squared, we can now write it as,
\[\Rightarrow \sqrt{{{\left( 13 \right)}^{2}}}\]
We can now write the radical symbol in terms of exponent, we get
\[\Rightarrow {{\left( 13 \right)}^{\dfrac{1}{2}\times 2}}\]
Here, we can now cancel the radical symbol square root which represent half in the exponent and the square inside the square root, we get
\[\Rightarrow 13\]
Therefore, the simplest radical form of \[\sqrt{169}\] is 13.

Note: Students should remember some of the perfect square numbers to simplify these types of problems. We should remember that we can now cancel the radical symbol square root which represents half in the exponent and the square inside the square root. We should know that If we only want the positive square root of a positive number then we use a radical sign, \[\sqrt{m}\], which denotes the positive square root of m. The positive square root is also called the principal square root.