Irrational numbers are any numbers that cannot be expressed as a quotient of two integers. Examples of irrational numbers include the square root of 2 and the square root of 30. To determine if a principal root is rational or irrational, check if the radicand is a perfect nth power - if it is, the root is rational, otherwise it is irrational. Estimating square roots involves finding the two closest perfect squares that are less than and greater than the number inside the radical.

1. Irrational
Numbers

2. Irrational numbers
are any number that
cannot be expressed
as a quotient of two
integer.

3. Examples:
a. √2
b. √30

4. To determine whether a
principal root is a rational or
irrational number, determine f
the radicand is a perfect nth
power or not. If it is, then the
root is rational otherwise it is
irrational.

5. Example:
a. ³√225
b. √0.04
c. √-111
irrational
rational
irrational

6. Find the two closest
perfect square that is
less than to the given
and greater to it.

7. Example:
a. √9
√16 ≤ √9 ≤ √25
4 5
Therefore √9 is between 4 and 5.

8. b. √60
c. √101

9. Estimate each square root to
the nearest tenth.
a. √40
b. √12
c. √175

10. Tell whether the principal roots of each
number is rational or irrational. And if its
irrational, estimate each square root to
the nearest tenth.
1. √25
2. √5o
3. √77
4. √90
5. √400

11. Assignment:
1.What is absolute value?
2.What is a Number line?
Elementary algebra 69-74