# Write in ascending order of the surds given in each of the following sets $\sqrt[4]{{625}},\sqrt[3]{{343}},\sqrt {100} $

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Hint: In this question we are provided with a term that is order of the surds mathematically it means that, in $\sqrt[n]{a}$, n is called the order of surd and a is called the radicand. After learning this we will pretty much be clear about our next step which involves dealing with roots and exponents then we have to arrange the data in ascending order which is when we move from smaller to the bigger number.

Complete step-by-step answer:

For solving the given question, we first must be aware of the order of a surd. The order of a surd indicates the index of a root to be extracted. In $\sqrt[n]{a}$, n is called the order of surd and a is called the radicand.

Now, coming back to the question we know we are given the following sets:

$

\sqrt[4]{{625}} = \sqrt[4]{{{{(5)}^4}}} = \sqrt[4]{{5 \times 5 \times 5 \times 5}} = 5 \\

\sqrt[3]{{343}} = \sqrt[3]{{{{(7)}^3}}} = \sqrt[3]{{7 \times 7 \times 7}} = 7 \\

\sqrt {100} = \sqrt {{{10}^2}} = \sqrt {10 \times 10} = 10 \\

$

Hence, the ascending order is 5<7<10.

Note: In this question one must note that we should know at first what order of a surd indicates the index of a root to be extracted. In $\sqrt[n]{a}$ , n is called the order of surd and a is called the radicand. Then once the basic is clear it is a very simple question which involves exponents and powers and nothing other than that also one must know what is ascending order in this type of arrangement we arrange going from the smaller value to the bigger keeping these small points in mind one should be able to solve the question.

Complete step-by-step answer:

For solving the given question, we first must be aware of the order of a surd. The order of a surd indicates the index of a root to be extracted. In $\sqrt[n]{a}$, n is called the order of surd and a is called the radicand.

Now, coming back to the question we know we are given the following sets:

$

\sqrt[4]{{625}} = \sqrt[4]{{{{(5)}^4}}} = \sqrt[4]{{5 \times 5 \times 5 \times 5}} = 5 \\

\sqrt[3]{{343}} = \sqrt[3]{{{{(7)}^3}}} = \sqrt[3]{{7 \times 7 \times 7}} = 7 \\

\sqrt {100} = \sqrt {{{10}^2}} = \sqrt {10 \times 10} = 10 \\

$

Hence, the ascending order is 5<7<10.

Note: In this question one must note that we should know at first what order of a surd indicates the index of a root to be extracted. In $\sqrt[n]{a}$ , n is called the order of surd and a is called the radicand. Then once the basic is clear it is a very simple question which involves exponents and powers and nothing other than that also one must know what is ascending order in this type of arrangement we arrange going from the smaller value to the bigger keeping these small points in mind one should be able to solve the question.

Last updated date: 01st Oct 2023

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