Approximating square roots walk through

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:

(\sqrt{25})^{2} = 25

(\sqrt{6})^{2} = 6

(\sqrt{9482})^{2} = 9482

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

Πρόβλημα 1Α

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

$\sqrt{30}$ ‍, $5$ ‍, $6$ ‍

Step 1: Square each of the numbers:

$n :$ ‍ $\sqrt{30}$ ‍ $5$ ‍ $6$ ‍
$n^{2} :$ ‍ $30$ ‍ $25$ ‍ $36$ ‍

$n :$ ‍	$\sqrt{30}$ ‍	$5$ ‍	$6$ ‍
$n^{2} :$ ‍	$30$ ‍	$25$ ‍	$36$ ‍

Step 2: Order the numbers from least to greatest:

$n :$ ‍ $5$ ‍ $\sqrt{30}$ ‍ $6$ ‍
$n^{2} :$ ‍ $25$ ‍ $30$ ‍ $36$ ‍

$n :$ ‍	$5$ ‍	$\sqrt{30}$ ‍	$6$ ‍
$n^{2} :$ ‍	$25$ ‍	$30$ ‍	$36$ ‍

The answer:

$5$ ‍ $\sqrt{30}$ ‍ $6$ ‍


$5$ ‍	$\sqrt{30}$ ‍	$6$ ‍

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

For example: $6, \sqrt{28}, 5$ ‍.

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

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

$? < \sqrt{97} < ?$ ‍

Step 1: Create a table of perfect squares.

$n :$ ‍ $7$ ‍ $8$ ‍ $9$ ‍ $10$ ‍ $11$ ‍
$n^{2} :$ ‍ $49$ ‍ $64$ ‍ $81$ ‍ $100$ ‍ $121$ ‍

$n :$ ‍	$7$ ‍	$8$ ‍	$9$ ‍	$10$ ‍	$11$ ‍
$n^{2} :$ ‍	$49$ ‍	$64$ ‍	$81$ ‍	$100$ ‍	$121$ ‍

Step 2: Ask yourself, "Where does

n = \sqrt{97}

fit into the table?"

$n :$ ‍ $7$ ‍ $8$ ‍ $9$ ‍ $\sqrt{97}$ ‍ $10$ ‍ $11$ ‍
$n^{2} :$ ‍ $49$ ‍ $64$ ‍ $81$ ‍ $97$ ‍ $100$ ‍ $121$ ‍

$n :$ ‍	$7$ ‍	$8$ ‍	$9$ ‍	$\sqrt{97}$ ‍	$10$ ‍	$11$ ‍
$n^{2} :$ ‍	$49$ ‍	$64$ ‍	$81$ ‍	$97$ ‍	$100$ ‍	$121$ ‍

Η απάντηση:

$9 < \sqrt{97} < 10$ ‍

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

< \sqrt{56} <

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