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 ?

Fill in the Blanks

√6 is between 2 and

.

Fill in the Blanks

√27 is between 5 and

.

Fill in the Blanks

√10 is between ___ and ____.

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

Fill in the Blanks

What is $\frac{3}{16}$ written as a decimal?

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.