Question

State the order of the surd given: \[\sqrt[4]{{10}}\]

Answer 1

Hint: Here, in the given question, we are asked to state the order of the given surd. Before solving this question, we must understand what a surd is, what is the order of the surd. Hence, we will first understand the definition and the meaning of the said terms and then solve for the required answer.

Complete step-by-step solution:
Definition of surd: The root of a positive real number is called a surd if its value cannot be exactly determined. In other words, surds are the roots of numbers that cannot be simplified into a whole or rational number. Usually, surds are the numbers that are irrational and cannot be represented as recurring decimals or as fractions.
Order of the surd: The order of a surd shows the index of root to be extracted. In \[\sqrt[n]{a}\], \[n\] is known as the order of a surd and \[a\] is called the radicand. Here, the index is\[n\]and hence, the order is \[n\].
Now, given surd, \[\sqrt[4]{{10}}\]
Index of the given surd is \[4\]
And, hence the order of the surd \[\sqrt[4]{{10}}\] is \[4\]

Note: Such type of questions does not require any formula. We just need to remember what a surd means, what an index of a square root is and what the order of the surd is. If we know about these terms, we can directly answer the questions by just looking at them. Also, we can write a \[{n^{th}}\] root in terms of power of something. For example: the given surd \[\sqrt[4]{{10}}\] can also be written as \[{10^{\dfrac{1}{4}}}\].