# ASCENDING AND DESCENDING ORDER OF SURDS

"Ascending and Descending Order of Surds" is the basic topic required for the students who would like to study Algebra in math.

## Ascending and descending order of surds:

Irrational numbers of same order can be compared. If we want to compare irrational numbers with different order we have convert them with same order and then we can compare. By comparing the surds we come to which radical term is greater or smaller.

## How to write irrational numbers in ascending and descending order of surds?

• Writing irrational numbers of same order from smaller to greater is known as "ascending order".
• Writing irrational numbers of same order from greater to smaller is known as "descending order".

## How to convert irrational numbers of same order?

(1) Write the orders of irrational numbers given

(2) Find the least common multiple.

(3) Make the order same.

(4) Now we can compare the radicands.

## Example problems of comparison of surds:

Problem 1:

Write the irrational numbers √3,∛2,∜4 in

(i) ascending order

(ii) descending order.

Solution:

Order of given irrational numbers are 2,3 and 4.

No we have to find the least common multiple

L.C.M = 12

In the next step we are going to change ∛2 as 12th root

now we are going to change the next term 4th root as 12th root

We have changed all the given radical terms with same order.

12th root (729) is the largest number

12th root (64) is the next least number and

12th root (16) is the most least number

Ascending order:

Ascending order means we have to write the number from least to greatest.

∛2 < ∜4 < √3

Descending order:

Descending order means we have to write the number from least to greatest.

√3 > ∜4 > ∛2

Now let us see the next example of the topic "ascending and descending order of surds"

Problem 2:

Write the irrational numbers ∜5,√3,∛4 in

(i) ascending order

(ii) descending order.

Solution:

Order of given irrational numbers are 4,2 and 3.

No we have to find the least common multiple

L.C.M = 12

In the next step we are going to change √3 as 12th root

In the next step we are going to change ∛4  as 12th root

We have changed all the given radical terms with same order.

12th root (729) is the largest number (second term)

12th root (256) is the next least number and (third term)

12th root (125) is the most least number (first term)

Ascending order:

Ascending order means we have to write the number from least to greatest.

√3, ∛4, ∜5

Descending order:

Descending order means we have to write the number from greatest to least.

∜5,∛4,√3

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