Everyone is irrational, sometimes.

Rational Numbers

100

What is a rational number?

A number that can be written as p/q where p and q are integers, q <> 0

200

True or false. Give reasons.

1. There can be infinitely many integers between two integers.

1. There can be infinitely many rational numbers between two integers.

1. False

2. True

300

If -7/x = -x/28, find the value of x.

-7/x = -x/28

=> -x² = -28*7

=> x² = 196 = 14²

=> x = 14

Irrational Numbers

100

What is the difference between a rational & an irrational number in decimal form?

A rational number can be written as a terminating or non-terminating repeating decimal number.

An irrational number is written as a non-terminating non-repeating decimal number.

200

D

300

If p = (1+√3)
Find the value of (p-1)/(p+1)

2√3 - 3

Mixed bag

100

Find the value of 16^1/4

2

200

Which is greater?

7/11 or 9/13

7/11 = (7*13)/(11*13) = 91/143

9/13 = (9*11)/(13*11) = 99/143

99/143 > 91/143

=> 9/13 > 7/11

300

Simplify: (1+√2)/(1−√2)

− (3 + 2√2)