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Μάθημα 4: Approximating irrational numbers

Approximating square roots walk through

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Walk through a series of questions and examples that will help you learn how to approximate square roots.

In this article, you'll learn how to approximate square roots! Let's dive in.

Παράδειγμα

Spot the pattern:

left parenthesis, square root of, start color #e07d10, 25, end color #e07d10, end square root, right parenthesis, squared, equals, start color #e07d10, 25, end color #e07d10

left parenthesis, square root of, start color #e07d10, 6, end color #e07d10, end square root, right parenthesis, squared, equals, start color #e07d10, 6, end color #e07d10

left parenthesis, square root of, start color #e07d10, 9482, end color #e07d10, end square root, right parenthesis, squared, equals, start color #e07d10, 9482, end color #e07d10

Ερώτηση αντανάκλασης

When you square the square root of a number...

Practice Set 1:

Πρόβλημα 1Α

Τρέχων

left parenthesis, square root of, 16, end square root, right parenthesis, squared, equals
Η απάντησή σου έπρεπε να είναι
ενας ακέραιος, όπως το 6
ένα απλοποιημένο σωστο κλάσμα, όπως το 3, slash, 5
ένα απλοποιημένο καταχρηστικό κλάσμα, όπως το 7, slash, 4
ένας μεικτός αριθμός, όπως το 1, space, 3, slash, 4
ένας ακριβής δεκαδικός, όπως το 0, point, 75
ένα πολλαπλάσιο του π, όπως το 12, space, start text, p, i, end text ή το 2, slash, 3, space, start text, p, i, end text

Παράδειγμα

Without using a calculator, order the following numbers from least to greatest.

square root of, 30, end square root, 5, 6

Step 1: Square each of the numbers:

n, colon square root of, 30, end square root 5 6
n, squared, colon start color #11accd, 30, end color #11accd start color #1fab54, 25, end color #1fab54 start color #ca337c, 36, end color #ca337c

n, colon	square root of, 30, end square root	5	6
n, squared, colon	start color #11accd, 30, end color #11accd	start color #1fab54, 25, end color #1fab54	start color #ca337c, 36, end color #ca337c

Step 2: Order the numbers from least to greatest:

n, colon 5 square root of, 30, end square root 6
n, squared, colon start color #1fab54, 25, end color #1fab54 start color #11accd, 30, end color #11accd start color #ca337c, 36, end color #ca337c

n, colon	5	square root of, 30, end square root	6
n, squared, colon	start color #1fab54, 25, end color #1fab54	start color #11accd, 30, end color #11accd	start color #ca337c, 36, end color #ca337c

The answer:

5 square root of, 30, end square root 6


5	square root of, 30, end square root	6

Ερώτηση αντανάκλασης

When ordering square roots and integers, which of the following is the best strategy?

For example: 6, comma, square root of, 28, end square root, comma, 5.

(Επιλογή Α)
Square just the square roots. For example: 6, comma, left parenthesis, square root of, 28, end square root, right parenthesis, start superscript, start color #e84d39, 2, end color #e84d39, end superscript, comma, 5.
(Επιλογή Β)
Square both the square roots and the integers. For example: 6, start superscript, start color #e84d39, 2, end color #e84d39, end superscript, comma, left parenthesis, square root of, 28, end square root, right parenthesis, start superscript, start color #e84d39, 2, end color #e84d39, end superscript, comma, 5, start superscript, start color #e84d39, 2, end color #e84d39, end superscript.

Practice Problem 2:

Without using a calculator, order the following numbers from least to greatest.

Παράδειγμα

Without using a calculator, find two consecutive integers to complete the following inequality.

question mark, is less than, square root of, 97, end square root, is less than, question mark

Step 1: Create a table of perfect squares.

n, colon 7 8 9 10 11
n, squared, colon 49 64 81 100 121

n, colon	7	8	9	10	11
n, squared, colon	49	64	81	100	121

Step 2: Ask yourself, "Where does n, equals, square root of, start color #1fab54, 97, end color #1fab54, end square root fit into the table?"

n, colon 7 8 start color #ca337c, 9, end color #ca337c square root of, start color #1fab54, 97, end color #1fab54, end square root start color #11accd, 10, end color #11accd 11
n, squared, colon 49 64 81 start color #1fab54, 97, end color #1fab54 100 121

n, colon	7	8	start color #ca337c, 9, end color #ca337c	square root of, start color #1fab54, 97, end color #1fab54, end square root	start color #11accd, 10, end color #11accd	11
n, squared, colon	49	64	81	start color #1fab54, 97, end color #1fab54	100	121

Η απάντηση:

start color #ca337c, 9, end color #ca337c, is less than, square root of, start color #1fab54, 97, end color #1fab54, end square root, is less than, start color #11accd, 10, end color #11accd

Practice Problem 3:

Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.

is less than, square root of, 56, end square root, is less than

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