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Course: Staging content lifeboat > Unit 15

Lesson 1: Square roots A
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Staging content lifeboat
Math
Square roots A
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Approximating square roots

Google Classroom

Introduction

In this article, you'll learn how to approximate square roots!

Part 1

Example

Watch what happens when we square the square root of a number:
(25)2=25
(6)2=6
(9482)2=9482

Reflection question

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

Practice

(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

(55)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

(8888)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

Part 2

Example

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

Reflection question

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

Practice

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

Part 3

Example

Without using a calculator, find consecutive whole numbers to complete the 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

Without using a calculator, fill in the blanks with two consecutive whole numbers 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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