Algebra I Recipe: Square Roots

A. Definitions

1. square rooting a number – finding the number that when multiplied by itself equals the number being square rooted.



2. perfect squares – numbers that can be square rooted evenly like 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, . . .
• 4 = 2 because 2 • 2 = 4, BUT it could also be = -2 because –2 • -2 = 4.
• 25 = 5 because 5 • 5 = 25, BUT it could also be = -5 because –5 • -5 = 25.
3. means to give the positive square root or answer. 81 = 9
4. -   means to give the negative square root or answer. -49 = -7
5. ± means to give the positive AND negative square root or answer.  ±25 = ± 5

B. Evaluating the Expression where a = 1, b = -2, c = -3

1. Substitute the values.
2. Follow order of operations to find the value of the expression under the .
3. Find the square root of the number.
• You cannot find the square root of a negative number.

C. Evaluating an Expression like

1. Make two problems.
• One with only the +
• One with only the -
2. Use order of operations to find the two values.
• Round the to the nearest hundredth when it cannot be square rooted evenly.

D. Pythagorean Theorem Right Triangle

1. Pythagorean Theorem is a² + b² = c².
2. The Pythagorean Theorem is used to find any missing side of a right triangle, when the other two lengths are known. It is also used to determine if three particular lengths would form a right triangle.
3. "a" and "b" are the legs that form the right angle.
4. "c" is the hypotenuse.

Practice Problems