Reasoning About Square Roots

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2019 Open Up Resources |

Let’s explore square
roots!

Today’s Goals

❏ I can find a decimal

approximation for square roots.

❏ I can plot square roots on the

number line.

❏ When I have a square root, I can

reason about which two whole
numbers it is between.

Squaring Lines

Comprehend/ Apply: Activity 4.2
● MLR8: Discussion Supports
● Anticipate, Monitor, Select, Sequence, Connect

If a number is not
rational, write it with
square root notation.

√17

Square Root of 3

Comprehend/ Apply: Activity 4.3
● Think Pair Share
● MLR1: Stronger and Clearer Each Time

What is the same
and what is different
about this diagram
and diagrams we’ve
seen in earlier
activities?

Begin working on
your own. (2-3 min)

Share your thinking
with your team.

Explain why 2.5 is
not a very good
approximation for
√3.

What is a good
approximation?

How can you approximate
the value of √130?
11² = 121
12² = 144

Organize: Lesson 4 Synthesis

So we know √130 is somewhere between
11 and 12.
Can we get more accurate than that? How?

We could try squaring numbers from
11 to 12, like 11.1, 11.2, etc., to find
the one closest to 130.

Let's Practice

Fill in the Blank

Consider the relationship shown.

What is the approximate value of √11 to the nearest whole number.

Multiple Choice

Tristan was chosen by his teacher to find the integer that has a square root closest to 3 without going over and write it on the board. Which correct answer did Tristan write on the board?

• 6

• 8

• 10

• 12

Multiple Choice

Between which two integers does the √55 lie?

• 11 and 12

• 9 and 10

• 7 and 8

• 5 and 6

Multiple Choice

The height of a triangle is given as √45. Between which two integers is the height of the triangle?

• 2 and 3

• 3 and 4

• 6 and 7

• 7 and 8

Square Root
Values

Apply/ Comprehend: Activity 5.2
●MLR3: Clarify, Critique, Correct

●Think Pair Share

Multiple Choice

A square has an area of 29 square inches. Which choice below is the best estimate for the side length of the square?

• More than 5 inches but less than 6 inches.

• More than 7 inches but less than 8 inches.

• More than 14 inches but less than 15 inches.

• More than 25 inches but less than 36 inches.

What two whole numbers does each
square root lie between? Be prepared to
explain your reasoning.
Begin working on your own. (2 min)
Compare your thinking with your team.

What strategy did
you use to figure
out the two whole

numbers?

Organize: Activity 5.2 Synthesis

Solutions on a
Number Line

Apply/ Comprehend: Activity 5.3

●

MLR1: Stronger and Clearer Each Time

●

Think Pair Share

Begin working on the task on your own. (2 min)
Compare your thinking with your team. Be prepared to
discuss your thinking with the whole class!

The numbers x, y, and z are positive, and x2 = 3, y2 = 16, and z2 = 30.

1. Plot x, y, and z on the number line.

2. Plot -√2 on the number line.

How can we find the whole numbers
that a square root lies between?

Look at the square of whole numbers
whose squares are greater than and
less than the number inside the
square root symbol, like 121 and 144
for √130.

Organize: Activity 5.3
Synthesis

How can we get a better
approximation?
Test value between
those two whole
numbers.

More Practice

Fill in the Blank

On a number line, which integer is closest to $$\sqrt[]{15}$$ ?

Dropdown

Select the point on the number line that best approximates the location of √38.​

Select answer

Multiple Choice

Between which two integers does √115 lie?

• 10 and 11

• 14 and 16

• 100 and 121

• 114 and 116

Multiple Choice

Between which two integers does √50 lie?

• 4 and 5

• 7 and 8

• 24 and 25

• 49 and 50

Multiple Choice

Explain why 9 is the best whole number estimate of √83.

• 83 is between 8² and 9² on the number line but is closer to 8².

• 83 is between 8² and 9² on the number line but is closer to 9².

• 83 is between 9² and 10² on the number line but is closer to 9².

• 83 is between 9² and 10² on the number line but is closer to 10².

Today’s Goals

❏ I can find a decimal

approximation for square roots.

❏ I can plot square roots on the

number line.

❏ When I have a square root, I can

reason about which two whole
numbers it is between.

Betweens

Apply/ Summarize:

Cool Down 5.4

Open Ended

Explain how you know.