## Finer grained standards that are part of this one

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., √57 lies between 7 and 8 since 7² = 49 and 8² = 64; −√11 lies between −4 and −3 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., √2 is an irrational number). An irrational number cannot be expressed exactly as a fraction 𝑎/𝑏 where 𝑏 does not equal 0.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

Square root symbols may be used to represent solutions to equations of the form 𝑥² = 𝑝.

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.