Section 1.3 Square Roots and Cube Roots

Flashcards testing concepts of square roots, cube roots, rational numbers, and irrational numbers from Section 1.3.

According to the tip in the text, what are natural numbers?

The natural numbers are the counting numbers and zero.

How many square roots does every positive integer have?

Every positive integer has two square roots, one positive and one negative.

Why does the integer $-25$ have no square root?

It has no square root because no negative number has a square root, meaning the equation $x^2 = -25$ has no solution.

Which natural numbers have integer square roots?

Only square numbers, such as $1, 4, 9, 16, 25...$, have integer square roots.

What does it mean for the square root of a natural number to be irrational?

It means that the square root cannot be written as a simple fraction or as a decimal without rounding.

What value does a calculator show for $√{2}$, and what is the result when that value is squared?

A calculator shows $√{2}$ as $1.414213562$, and when this number is squared, the result is $1.999999999$.

How many cube roots does every number (positive, negative, or zero) have?

Every number, positive or negative or zero, has only one cube root.

What is the cube root of $-125$, written as $∛{-125}$, and how is it calculated?

The value is $-5$, calculated as $(-5)^3 = -5 \times -5 \times -5 = (-5 \times -5) \times -5 = 25 \times -5 = -125$.