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 goldD, 25, end color goldD, end square root, right parenthesis, start superscript, 2, end superscript, equals, start color goldD, 25, end color goldD
left parenthesis, square root of, start color goldD, 6, end color goldD, end square root, right parenthesis, start superscript, 2, end superscript, equals, start color goldD, 6, end color goldD
left parenthesis, square root of, start color goldD, 9482, end color goldD, end square root, right parenthesis, start superscript, 2, end superscript, equals, start color goldD, 9482, end color goldD

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, start superscript, 2, end superscript, 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, p, i or 2, slash, 3, space, p, i

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, space, space, colonsquare root of, 30, end square root56
n, start superscript, 2, end superscript, colonstart color blueD, 30, end color blueDstart color greenD, 25, end color greenDstart color maroonD, 36, end color maroonD
Step 2: Order the numbers from least to greatest:
n, space, space, colon5square root of, 30, end square root6
n, start superscript, 2, end superscript, colonstart color greenD, 25, end color greenDstart color blueD, 30, end color blueDstart color maroonD, 36, end color maroonD
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.
  • 4
  • square root of, 14, end square root
  • 5

Example

Without using a calculator, find two consecutive integers to complete the following inequality.
question mark, space, is less than, square root of, 97, end square root, is less than, space, question mark
Step 1: Create a table of perfect squares.
n, space, space, colon7891011
n, start superscript, 2, end superscript, colon496481100121
Step 2: Ask yourself, "Where does n, equals, square root of, start color greenD, 97, end color greenD, end square root fit into the table?"
n, space, space, colon78start color maroonD, 9, end color maroonDsquare root of, start color greenD, 97, end color greenD, end square rootstart color blueD, 10, end color blueD11
n, start superscript, 2, end superscript, colon496481start color greenD, 97, end color greenD100121
The answer:
start color maroonD, 9, end color maroonD, is less than, square root of, start color greenD, 97, end color greenD, end square root, is less than, start color blueD, 10, end color blueD

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, p, i or 2, slash, 3, space, p, i
space, is less than, square root of, 56, end square root, is less than, space
  • 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, p, i or 2, slash, 3, space, p, i