COMPARISON OF SURDS
"Comparison of Surds" is the basic topic required for the students who would like to study Algebra in math.
What is comparison 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 irrational number is greater or smaller.
What has to be done?
(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 comparision 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 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
Related topics of "comparison of surds"
- Simplifying radical expressions
- Radical
- Like terms and unlike terms
- Markup and markdown
- Percents grater than 1
WORD PROBLEMS
HCF and LCM 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
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
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
