"Comparison of Surds" is the basic topic required for the students who would like to study Algebra in math.

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 irrational number is greater or smaller.

(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.

**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 greatest to least.

√3 > ∜4 > ∛2

Now let us see the next example of the topic "comparison of surds"

**Problem 2:**

Which is greater ∛4 or ∜5

**Solution:**

Order of given radical terms are 3 and 4.

To make the orders same we have to take L.C.M

L.C.M = 12

∛4 = (3 x 4) √4⁴

∛4 = 12th root(4 x 4 x 4 x 4)

= 12th root (256)

∜5 = (4 x 3) √5³

∜5 = 12th root(5 x 5 x 5)

= 12th root (125)

12th root (256) > 12th root (125)

∛4 > ∜5

∛4 is greater than ∜5.

Now let us see the next example of the topic "comparison of surds"

**Problem 3:**

Which is greater ∛3 or √2

**Solution:**

Order of given radical terms are 3 and 2.

To make the orders same we have to take L.C.M

L.C.M = 6

∛3 = (3 x 2) √2²

∛3 = 6th root(2 x 2)

= 6th root (4)

√2 = (2 x 3) √2³

√2 = 6th root(2 x 2 x 2)

= 6th root (8)

6th root (8) > 6th root (4)

√2 > ∛3

√2 is greater than ∛3

Now let us see the next example of the topic "comparison of surds"

**Problem 4:**

Which is greater ∛3 or ∜4

**Solution:**

Order of given radical terms are 3 and 4.

To make the orders same we have to take L.C.M

L.C.M = 12

∛3 = (3 x 4) √3⁴

∛3 = 12th root(3 x 3 x 3 x 3)

= 12th root (81)

∜4 = (4 x 3) √4³

∜4 = 12th root(4 x 4 x 4)

= 12th root (64)

12th root (81) > 12th root (64)

∛3 > ∜4

∜4 is greater than ∛3

Now let us see the next example of the topic "comparison of surds"

**Problem 5:**

Which is greater ∛3 or ∜10

**Solution:**

Order of given radical terms are 3 and 4.

To make the orders same we have to take L.C.M

L.C.M = 12

∛3 = (3 x 4) √3⁴

∛3 = 12th root(3 x 3 x 3 x 3)

= 12th root (81)

∜10 = (4 x 3) √10³

∜10 = 12th root(10 x 10 x 10)

= 12th root (1000)

12th root (1000) > 12th root (81)

∜10 > ∛3

∜10 is greater than ∛3

- Simplifying radical expressions
- Radical
- Like terms and unlike terms
- Markup and markdown
- Percents grater than 1

Widget is loading comments...

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**