Rational Exponents 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: 2 Since 14 = 196 14 − 81

PDF page 1043: The negative is in front of the radical sign. −9 − 289

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 1045: Locate 60 between two consecutive perfect squares.

PDF page 1045: 60 is between their square roots.

PDF page 1045: There are mathematical methods to approximate square roots, but nowadays most people use a calculator to find them. Find the x key on your calculator. You will use this key to approximate square roots. When you use your calculator to find the square root of a number that is not a perfect square, the answer that you see is not the exact square root. It is an approximation, accurate to the number of digits shown on your calculator’s display. The symbol for an approximation is ≈ and it is read ‘approximately.’ Suppose your calculator has a 10-digit display. You would see that

PDF page 1045: EXAMPLE 9.5 Round 17 to two decimal places. Solution 17 Use the calculator square root key. 4.123105626... Round to two decimal places. 4.12 17 ≈ 4.12