Compare Irrational Numbers
Compare Irrational Numbers
We have already discussed Rational and Irrational Numbers, so now let us take a look on how to compare irrational numbers.
Irrational numbers include numbers which are not perfect square roots or perfect cube roots and can’t be found out exactly.
For Example , , ,, , , are not perfect square roots.
Similarly , , , , , , are not perfect cube roots, and hence irrational.
- To compare two irrational numbers which are of the first form , say and we find the square of both numbers and compare them
For Example: = x = 3,
= x = 5 and since 3 < 5 hence < .
- To compare two irrational numbers which are of the second form, say and we find the cube of both numbers and compare them.
For Example: = x x = 2,
= x x = 3 and since 2 < 3 hence < .
For Example Consider and
= x x x x = 15,
= x x x x = 21 and 15 < 21 hence < .
- Which of the two numbers is greater? or
- Which of the two numbers is smaller? or
- Insert appropriate symbol > or < between the given numbers: ,
- Arrange the following numbers in ascending order of their magnitudes:
- Arrange the following numbers in descending order of their magnitudes:
- < .
- < < .
- > > .
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The Number System
Expressions and Equations
1) Exponents and their properties
2) Square roots and Cube roots
3) Scientific Notation – addition, subtraction, division and multiplication
4) Equations with variables on both sides
5) Linear equations with one, zero, or infinite solutions
6) Age Word Problems
7) Solve systems of linear equations with elimination and substitution
8) Word Problems on System of Linear Equations