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Estimating Square Roots

This topic covers estimating square roots to a given number of decimal places and solving problems using estimation of square roots.

Topic: Estimate Square Roots

  • We can use the square roots of perfect squares to help estimate the square roots of other numbers

  • √a (‘a’ is not a perfect square) is between two perfect squares that are close to ‘a’.
    For example: √40 is between the perfect squares 36 and 49

  • If ‘√a’ is between b and c, then the best estimate of √a to the nearest whole number is the number it is more closer to.
    For example: Best estimate of √40 to the nearest whole number is 6, since 40 is closer to 36(62) than 49 (72)

  • If a < x < b, then –a > -x > -b

Topic: Number Line to Find Square Roots

  • We can use the square roots of perfect squares to help estimate the square roots of other numbers

  • √a (‘a’ is not a perfect square) is between two perfect squares that are close to ‘a’. For example: √40 is between the perfect squares 36 and 49

  • If ‘√a’ is between b and c, then the best estimate of √a to the nearest whole number is the number it is more closer to.
    For example: best estimate of √40 to the nearest whole number is 6, since 40 is closer to 36(62) than 49 (72)

Topic: Application Problems

  • We can use the square roots of perfect squares to help estimate the square roots of other numbers

  • √a (‘a’ is not a perfect square) is between two perfect squares that are close to ‘a’. For example: √40 is between the perfect squares 36 and 49

  • We can use the square roots to estimate side length of a square, when the area is given
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