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Exploring Square Numbers and Square Roots

This lesson focuses on understanding square numbers and their roots, specifically perfect squares up to 400. Students will learn to identify perfect squares, calculate their roots, and explore non-perfect squares. Through exercises, students will find square roots of both types, identify the dimensions of squares, and work on practical applications, such as determining the side length of a patio based on area. Engaging visuals and hands-on activities will enhance comprehension and retention.

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Exploring Square Numbers and Square Roots

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  1. Today’s lesson . . . What: Square numbers and Square roots Why: To examine the perfect square numbers up to 400 and to find the square root of both perfect and non-perfect square numbers.

  2. This square represents which perfect square #?_______ This is also the __________ of the square. The square root of this square is _________ because it is a 4 x 4 square. The square root is the ____________ length of the square. 16 area 4 side

  3. = 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 10 = 11 = 12 = 13 = 14 = 15 = 16 = 17 = 18 = 19 = 20

  4. The PERFECT SQUARE # is the __________ of the square!!! AREA The SQUARE ROOT # represents the __________ length of the square!!! SIDE

  5. Perfect square EXAMPLES: √64 = 2. √225 = 3. √ 36 = 4. √ 169 = 8 15 6 13 5. √ 400 = 6. √ 25 = 20 5

  6. NON-PERFECT SQUARE # EXAMPLES: Between which two consecutive whole numbers do the following #’s fall between? √22 lies between _____ and _____. √54 lies between _____ and _____. 4 5 8 7 3. √133 lies between _____ and _____. 4. √320 lies between _____ and _____. 12 11 17 18

  7. Math -7NOTES DATE: ______/_______/_______ NAME: What: Square numbers and square roots Why: To examine the perfect square numbers up to 400 and to find the square root of both perfect and non-perfect square numbers. This square represents which perfect square #?_______ This is also the __________ of the square. The square root of this square is ________because it is a 4 x 4 square. The square root is the ____________ length of the square. = 1 The PERFECT SQUARE # is the __________ of the square!!! = 2 The SQUARE ROOT # represents the __________ length of the square!!!

  8. Perfect square EXAMPLES: √64 = 2. √225 = 3. √ 36 = 4. √ 169 = 5. √ 400 = 6. √ 25 = NON-PERFECT SQUARE # EXAMPLES: Between which two consecutive whole numbers do the following #’s fall between? √22 lies between _____ and _____. √54 lies between _____ and _____. 3. √133 lies between _____ and _____. 4. √320 lies between _____ and _____.

  9. NAME:________________________________________________________________________________DATE: _____/_____/__________ PRACTICE WORK “Square roots and perfect square numbers” Find the square root of the following numbers: Between which two consecutive WHOLE numbers do the following #’s fall between?: Short Answer: Draw a picture that models the following perfect square number: 9 Jerry is designing a square patio. The patio has an area of 98 square feet. About how long is each side of the patio? What perfect square # does the square to the right represent? __________ What would its square root be (square to the right)? __________

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