1. Find the lengths (in units) of the unlabeled sides.

   

   

2. One segment is \(n\) units long and the other is \(p\) units long. Find the value of \(n\) and \(p\). (Each small grid square is 1 square unit.)

   

   A line segment labeled “n” on a square grid. The line segment starts at an intersection point on the grid and slants downward and to the right to an end point that is 1 unit to the right and 3 units down.

   

   A line segment labeled “p” on a square grid. The line segment starts at an intersection point on the grid and slants upward and to the right to an end point that is 3 units to the right and 4 units up.

Use the areas of the two identical squares to explain why \(5^2+12^2=13^2\) without doing any calculations.

2 decomposed squares. On left square is decomposed into square with side length = 5, 2 rectangles with sides = 12 and 5, and square with side length = 12. On right square is decomposed into a square with side length = 13 and 4 right triangles with sides = 5, 12, 13.

Each number is between which two consecutive integers?

1. \(\sqrt{10}\)
2. \(\sqrt{54}\)
3. \(\sqrt{18}\)
4. \(\sqrt{99}\)
5. \(\sqrt{41}\)

1. Give an example of a rational number, and explain how you know it is rational.
2. Give three examples of irrational numbers.

Write each expression as a single power of 10.

1. \(10^5 \boldcdot 10^0\)

2. \(\dfrac{10^9}{10^0}\)

Andre is ordering ribbon to make decorations for a school event. He needs a total of exactly 50.25 meters of blue and green ribbon. Andre needs 50% more blue ribbon than green ribbon for the basic design, plus an extra 6.5 meters of blue ribbon for accents. How much of each color of ribbon does Andre need to order?