8.3 The student will a) estimate and determine the two consecutive integers between which a square root lies; and b) determine both the positive and negative square roots of a given perfect square. Understanding the Standard Essential Knowledge and Skills The student will use problem solving, mathematical A perfect square is a whole number whose square root is an integer. communication, mathematical reasoning, connections, and The square root of a given number is any number which, when multiplied times itself, equals the representations to given number. Estimate and identify the two consecutive integers between Both the positive and negative roots of whole numbers, except zero, can be determined. The square which the positive or negative square root of a given number root of zero is zero. The value is neither positive nor negative. Zero (a whole number) is a perfect lies. Numbers are limited to natural numbers from 1 to 400. (a) square. Determine the positive or negative square root of a given perfect The positive and negative square root of any whole number other than a perfect square lies between square from 1 to 400. (b) two consecutive integers (e.g., lies between 7 and 8 since 72 = 49 and 82 = 64; lies between -4 and - since (-4)2 = 16 and (-3)2 = 9). The symbol may be used to represent a positive (principal) root and may be used to represent a negative root. The square root of a whole number that is not a perfect square is an irrational number (e.g., is an irrational number). An irrational number cannot be expressed exactly as a fraction where does not b equal 0. Square root symbols may be used to represent solutions to equations of the form = Examples x2 p. may include: If = 36, then is = 6 or =-6. x2 x If = 5, then is or x2 x −. Students can use grid paper and estimation to determine what is needed to build a perfect square. The square root of a positive number is usually defined as the side length of a square with the area equal to the given number. If it is not a perfect square, the area provides a means for estimation.
8.3 The student will a) estimate and determine the two consecutive integers between which a square root lies; and b) determine both the positive and negative square roots of a given perfect square. Understanding the Standard Essential Knowledge and Skills A perfect square is a whole number whose square root is an integer. The square root of a given number is any number which, when multiplied times itself, equals the given number. Both the positive and negative roots of whole numbers, except zero, can be determined. The square root of zero is zero. The value is neither positive nor negative. Zero (a whole number) is a perfect square. The positive and negative square root of any whole number other than a perfect square lies between two consecutive integers (e.g., lies between 7 and 8 since 72 = 49 and 82 = 64; lies between -4 and since (-4)2 = 16 and (-3)2 = 9). The symbol may be used to represent a positive (principal) root and - may be used to represent a negative root. The square root of a whole number that is not a perfect square is an irrational number (e.g., is an irrational number). An irrational number cannot be expressed exactly as a fraction where b does not equal 0. Square root symbols may be used to represent solutions to equations of the form x2 = p. Examples may include: If x2 = 36, then x is = 6 or =-6. If x2 = 5, then x is or −. Students can use grid paper and estimation to determine what is needed to build a perfect square. The square root of a positive number is usually defined as the side length of a square with the area equal to the given number. If it is not a perfect square, the area provides a means for estimation. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Estimate and identify the two consecutive integers between which the positive or negative square root of a given number lies. Numbers are limited to natural numbers from 1 to 400. (a) Determine the positive or negative square root of a given perfect square from 1 to 400. (b)
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