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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.

Example

Spot the pattern:
(25)2=25
(6)2=6
(9482)2=9482

Reflection question

When you square the square root of a number...
Choose 1 answer:

Practice Set 1:

Problem 1A

(16)2=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Example

Without using a calculator, order the following numbers from least to greatest.
30, 5, 6
Step 1: Square each of the numbers:
n:3056
n2:302536
Step 2: Order the numbers from least to greatest:
n:5306
n2:253036
The answer:
5306

Reflection question

When ordering square roots and integers, which of the following is the best strategy?
For example: 6,28,5.
Choose 1 answer:

Practice Problem 2:

Without using a calculator, order the following numbers from least to greatest.
1

Example

Without using a calculator, find two consecutive integers to complete the following inequality.
?<97<?
Step 1: Create a table of perfect squares.
n:7891011
n2:496481100121
Step 2: Ask yourself, "Where does n=97 fit into the table?"
n:789971011
n2:49648197100121
The answer:
9<97<10

Practice Problem 3:

Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
<56<
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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