Monday 12/9 Exponents, Roots, and Real Number System

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a fraction of two integers. Examples include non-perfect squares like √2 or √3.

Front

What is a rational number?

Back

A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b is not zero. Examples include fractions like 1/2, whole numbers like 3, and perfect squares like √16.

Front

What is the rule for dividing exponents with the same base?

Back

When dividing exponents with the same base, subtract the exponent in the denominator from the exponent in the numerator. For example, a^m / a^n = a^(m-n).

Front

What is the value of 8⁷ ÷ 8²?

Back

8⁵

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. For example, √16 = 4 because 4 × 4 = 16.

Front

What is the approximate value of √200?

Back

√200 is approximately between 14 and 15.

Front

What is the rule for multiplying exponents with the same base?

Back

When multiplying exponents with the same base, add the exponents. For example, a^m × a^n = a^(m+n).

Front

What is the value of n² ⋅ n⁴ ⋅ n⁵?

Back

n¹¹

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. Examples include 1, 4, 9, 16, and 25.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as such. For example, 1/2 is rational, while √2 is irrational.