Simplify and Use Square Roots Quiz

PDF page 1042: Sometimes we will need to look at the relationship between numbers and their squares in reverse. Because 225 is the square of 15, we can also say that 15 is a square root of 225. A number whose square is m is called a square root of m .

PDF page 1042: 2 Notice (−15) = 225 also, so −15 is also a square root of 225. Therefore, both 15 and −15 are square roots of 225. So, every positive number has two square roots—one positive and one negative. What if we only wanted the positive square root of a positive number? The radical sign, m , denotes the positive square root. The positive square root is also called the principal square root. 2 We also use the radical sign for the square root of zero. Because 0 = 0 , 0 = 0 . Notice that zero has only one square root.

PDF page 1042: 2 Notice (−15) = 225 also, so −15 is also a square root of 225. Therefore, both 15 and −15 are square roots of 225. So, every positive number has two square roots—one positive and one negative. What if we only wanted the positive square root of a positive number? The radical sign, m , denotes the positive square root. The positive square root is also called the principal square root. 2 We also use the radical sign for the square root of zero. Because 0 = 0 , 0 = 0 . Notice that zero has only one square root.

PDF page 1042: 2 Notice (−15) = 225 also, so −15 is also a square root of 225. Therefore, both 15 and −15 are square roots of 225. So, every positive number has two square roots—one positive and one negative. What if we only wanted the positive square root of a positive number? The radical sign, m , denotes the positive square root. The positive square root is also called the principal square root. 2 We also use the radical sign for the square root of zero. Because 0 = 0 , 0 = 0 . Notice that zero has only one square root.

PDF page 1042: 2 Notice (−15) = 225 also, so −15 is also a square root of 225. Therefore, both 15 and −15 are square roots of 225. So, every positive number has two square roots—one positive and one negative. What if we only wanted the positive square root of a positive number? The radical sign, m , denotes the positive square root. The positive square root is also called the principal square root. 2 We also use the radical sign for the square root of zero. Because 0 = 0 , 0 = 0 . Notice that zero has only one square root.

PDF page 1043: EXAMPLE 9.1 Simplify: a 36 b 196 c − 81 d − 289 . Solution 36

PDF page 1043: 2 Since 6 = 36 6 196

PDF page 1043: 2 Since 14 = 196 14 − 81

PDF page 1043: The negative is in front of the radical sign. −17

PDF page 1043: There is no real number whose square is −169. −169 is not a real number.

PDF page 1043: When using the order of operations to simplify an expression that has square roots, we treat the radical as a grouping symbol. EXAMPLE 9.3 Simplify: a 25 + 144 b 25 + 144 . Solution

PDF page 1044: Simplify under the radical sign. 169

PDF page 1044: Simplify. 13 Notice the different answers in parts a and b!

PDF page 1044: EXAMPLE 9.4 Estimate 60 between two consecutive whole numbers. Solution

PDF page 1045: Locate 60 between two consecutive perfect squares.