7th Grade Math

Square Roots

PART A B C DE

Multi-Part

Lesson 3

Get ConnectED

GLE 0706.2.5

Understand and work with

squares, cubes, square roots

and cube roots. SPI 0706.2.4

Determine the approximate

location of square/cube roots

on a number line. Also

addresses GLE 0706.1.2,

GLE 0706.1.8, SPI 0706.2.3.

Lesson 3C Square Roots 57

Estimate Square Roots

Estimate the square root of 27.

• Arrange 27 tiles into the largest square
  possible.


• Add tiles to make the next larger
  square.


• The square root of 27 is between 5 and 6.
  Since 27 is much closer to 25 than 36, the
  square root of 27 is closer to 5 than 6.

Use algebra tiles to estimate the square root

of each number to the nearest whole number.

1. 40 2. 28 3. 85 4. 62


2. Describe another method that you could use to estimate the
   square root of a number.

The square root of a perfect square is an integer. You can estimate the

square root of a number that is not a perfect square.

Estimate a Square Root

Estimate √ 78 to the nearest whole number.

List some perfect squares. 1, 4, 9, 16, 25, 36,

49, 64, 81, ...

The first perfect square less than 78 is 64. √  64 = 8

The first perfect square more than 78 is 81. √  81 = 9

678

64 78 81

910

So, √78 is between 8 and 9. Since 78 is much closer to 81 than to

64, the best whole number estimate is 9. Verify with a calculator.

a. Estimate √ 50 to the nearest whole number.

Main Idea

Estimate square roots.

Vocabulary

irrational number

cube root

V

i

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