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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:
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

Reflection question

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

Practice Set 1:

Problem 1A

left parenthesis, square root of, 16, end square root, right parenthesis, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Example

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, colonsquare root of, 30, end square root56
n, squared, colonstart color #11accd, 30, end color #11accdstart color #1fab54, 25, end color #1fab54start color #ca337c, 36, end color #ca337c
Step 2: Order the numbers from least to greatest:
n, colon5square root of, 30, end square root6
n, squared, colonstart color #1fab54, 25, end color #1fab54start color #11accd, 30, end color #11accdstart color #ca337c, 36, end color #ca337c
The answer:
5square root of, 30, end square root6

Reflection question

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.
Choose 1 answer:
Choose 1 answer:

Practice Problem 2:

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

Example

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, colon7891011
n, squared, colon496481100121
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, colon78start color #ca337c, 9, end color #ca337csquare root of, start color #1fab54, 97, end color #1fab54, end square rootstart color #11accd, 10, end color #11accd11
n, squared, colon496481start color #1fab54, 97, end color #1fab54100121
The answer:
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.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
is less than, square root of, 56, end square root, is less than
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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