Unit 2 Math 8A Square Roots

Multiple Choice

Warm up:

6² =

• 12

• 8

• 36

• 62

Multiple Choice

$$\sqrt[]{36}$$

• 16

• 12

• 6

• 9

Sets of Numbers

Number Sets and Hierarchy

Hierarchy (ranking greatest to least)

All integers, whole numbers, and natural numbers are also Rational. Their circles fit inside the Rational set's circle.

​All ________ are also ___________.

Some _______ are also __________.

Not all _______ are ________.


The number _____ is rational and whole.

_____ is a fraction, but it is not a rational number.

Categorize

Options (18)

$$\sqrt[]{3}$$  

$$\sqrt[]{2}$$  

$$\pi$$  

$$-3$$

$$2\ \frac{1}{2}$$  

0.3333333...

$$0.\overline{15}$$  

$$\frac{\pi}{2}$$  

$$-\frac{7}{100}$$  

-17

0

6

1,225

19.56

$$\sqrt[]{9}$$  

$$\sqrt[]{25}$$  

$$\sqrt[]{100}$$  

$$\sqrt[]{11}$$  

Organize these options into the right categories

Integers

Irrational Numbers

Non-Integer Rational Numbers

Drag and Drop

All whole numbers are also ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

integers

natural numbers

irrational nubmers

Drag and Drop

All ​ integers are also ​ ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

natural numbers

rational numbers

whole numbers

Drag and Drop

Some ​

Placeholder

are also ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

rational numbers

integers

irrational

Find 2 perfect square numbers the number under the radical is between.

ex. √12 is between _____ and _____

​

How to estimate square roots.

​Because 48 is between 36 and 49, its square root will be between √​36 and √49.

It should be between 6 and 7, but closer to 7. Check it in a calculator!

Between what 2 consecutive integers is √48?

Between what 2 consecutive integers is √11 ?

Converting between fractions and repeating decimals.

​

Rational Numbers in different forms

Fractions mean division

Top ÷ Bottom
(numerator ÷denominator)

​

Fraction to decimal

Multiple Choice

Write the fraction as a decimal: $$\frac{2}{5}$$

• That is 2 ÷ 5

• That is 5 ÷ 2

• That is 0.25

Multiple Choice

Write the fraction as a decimal: $$\frac{1}{3}$$

• That is 1 ÷ 3 = 0.3

• That is 1 ÷ 3 = 0.33333...

• That is 0.13

1. Look at the repeating part. Count the number of digits.

2. Put that many 9s in the denominator.

3. Write the repeating part in the numerator.

4. Simplify.

​

Rewrite a repeating decimal as a fraction

1. Look at the repeating part. Count the number of digits.

2. Put that many 9s in the denominator.

3. Write the repeating part in the numerator.

4. Simplify.

​

Rewrite 0.121212... as a fraction in simplest form.

Getting between numbers

The space between 1 and 2 is infinite.