SPI 2.2 Rational and Irrational Numbers Coach Lesson 1

Question 1

1

Name the first 12 perfect squares.

Answer 1

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

How to determine any perfect square.

1x1 = 1² = 1

2x2 = 2² = 4

3x3 = 3² = 9

n x n = n²

Question 2

2

Name the first 5 perfect cubes.

Answer 2

1, 8, 27, 64, 125.

How to determine any perfect cube:

1x1x1 = 1³ = 1

2x2x2 = 2³ = 8

3x3x3 = 3³ = 27

n x n x n = n³

Question 3

3

What are non-perfect squares?

Answer 3

Numbers like 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, and 17.

• These are non-perfect squares because no whole number times its exact self is equal to these numbers.

Question 4

4

EX 1: How do you simplify a number that has an exponent of 2?

• For a base of 5 with an exponent of 2?

Answer 4

Multiply that base number times itself.

• 5 x 5 = 25

Question 5

5

EX 2: How do you take the square root of a perfect square?

• For example, the square root of 81?

Answer 5

Determine what number times itself is equal to the perfect square.

• Because 9 x 9 = 81, the square root of 81 is 9.

Question 6

6

EX 3: How do I determine which two whole numbers a square root lies between?

• For example, the square root of 17 lies between which two whole numbers?

Answer 6

1. Determine which two perfect squares the number lies between.
   * 17 lies between 16 and 25.
2. Take the square root of each of those numbers.

• The square root of 16 is 4; the square root of 25 is 5.
• Therefore the square root of 17 is between 4 and 5.

Question 7

7

EX 4: How do I find the square root of a non-perfect square and round it to the nearest tenth of nearest hundredth?

• For example, the square root of 43 rounded to the nearest tenth and the nearest hundredth?

Answer 7

1. Using a calculator, determine the square root.
   * The square root of 43 is 6.5574385…
2. Round to the specified place value.

• Rounded to the nearest tenth it is 6.6.
• Rounded to the nearest hundredth, it is 6.56.

Question 8

8

EX 5: How do you simplify the square root of a non-perfect square using prime factorization?

• For example, simplify the square root 99; write answer as with a radical.

Answer 8

1. Factor out the largest perfect square factor of a number.

• 9 is the largest perfect square factor of 99
• 99 is 9 x 11
• The square root of 9 is 3.
• 11 is not a perfect square so it stays under the radical.

2. Take the square root of that largest perfect square and write it on the outside of the radical sign–leave the other factor inside the radical sign.
   * 99 is equal to 3 times the square root of 11