Unit 1 Challenge 3 PDF

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Which of the following would result in an integer?  a.)

The square root of 144 is the only number that results in an integer because it is a perfect square. 144 can be rewritten as 12*12.

Which of the following would result in an integer?

The cube root of 27 is the only number that results in an integer because it is a perfect cube. 27 can be rewritten as 3*3*3.

Which of the following would result in an integer? The square root of 169 is the only number that results in an integer because it is a perfect square. 169 can be rewritten as 13*13.

Evaluate the following radical.

When evaluating a cube root, you need to find a number that can be multiplied by itself three times to equal the number under the radical. In this case, 5 can be multiplied three times to equal 125: 5*5*5 = 125. So the cube root of 125 is 5.

Evaluate the following radical.

c.)



When evaluating a cube root, you need to find a number that can be multiplied by itself three times to equal the number under the radical. In this case, -3 can be multiplied three times to equal -27: (-3)*(-3)*(-3) = -27. So the cube root of -27 is -3.

Evaluate the following radical.

Negatives have no square roots because if we square a positive or a negative, the answer will be positive (or zero). You can only take the square root of non-negative numbers.

Simplify the following radical expression.

When simplifying radical expressions, it is helpful to look for perfect squares. The

can be expressed as

Roots, this can be rewritten as

. Using the Product Property of Square . The

is equal to 3 and

be broken down any further with perfect squares, so the solution is

cannot .

Simplify the following radical expression.

When simplifying radical expressions, it is helpful to look for perfect squares. The

can be expressed as

Roots, this can be rewritten as

. Using the Product Property of Square . The

is equal to 2 and

be broken down any further with perfect squares, so the solution is Simplify the following radical expression.



a.)

cannot .

When simplifying radical expressions, it is helpful to look for perfect squares. The

can be expressed as

Roots, this can be rewritten as

. Using the Product Property of Square The

is equal to 5 and

be broken down any further with perfect squares, so the solution is

cannot .

Simplify the following radical expression.

To simplify the square root, the Product Property and Quotient Property is applied to break down each term under the square root. Next, simplify by evaluating each square root: it is not possible to take the square root of x so this stays as of

, the square root

is y, and the square root of 16 is 4. Finally, put all three parts together.

Simplify the following radical expression.



To simplify the cube root, the Product Property is applied to break down each term under the cube root. Next, simplify by evaluating each cube root: the cube root of 8 is 2; it is not possible to take the cube root of just x so this will stay as

; and the cube root of

is y. Finally, put all three parts together.

Simplify the following radical expression.

One side of a laptop is 9.5 inches and the other side is 14 inches. Using the Pythagorean Theorem, what is the length of the diagonal of the laptop? Answer choices are rounded to the nearest inch.  d.) 17 inches The Pythagorean Theorem is used to find the diagonal of a rectangle when the two sides are given. Recall that the formula is: , where a and b are the side lengths and c is the diagonal length. Plug in 9.5 and 14 in for a and b and solve for c.

The diagonal is approximately 17 inches.

A rectangular table is 22.5 inches wide and 31 inches long. Using the Pythagorean Theorem, what is the length of the diagonal of the table? Answer choices are rounded to the nearest inch. 38 inches

The equation , where r represents radius and h represents height, is used to find the volume of a ________. cylinder

The equation , where b represents base and h represents height, is used to find the area of a ________. triangle Betty has the option of using three types of tables in her coffee shop: square tables with a side length of 36 inches rectangular tables 20 inches wide and 73 inches long round (circular) tables with a diameter of 42 inches. Which type of table has the largest area? Rectangular tables The rectangular table has the largest area. The area of the rectangular table is

.

The square table has an area of

.

To find the area of the round table, you first need to find the radius by dividing the diameter in half: r = diameter ÷ 2 = 42 ÷ 2 = 21. The round table has an area of

.

Brad has the option of using three types of tables in his bagel shop: square tables with a side length of 39 inches rectangular tables 23 inches wide and 71 inches long round (circular) tables with a diameter of 48 inches. Which type of table has the largest area? Round tables The round table has the largest area. To find the area of the round table, you first need to find the radius by dividing the diameter in half: r = diameter ÷ 2 = 48 ÷ 2 = 24. The area of the round table is pi x 24 x 24 = 1810in squared..

The rectangular table has an area of 23 x 71 = 1633 in squared. The square table has an area of 39 x 39 = 1521 in squared

Barbara has the option of using three types of tables in her ice cream shop: square tables with a side length of 44 inches rectangular tables 26 inches wide and 73 inches long round (circular) tables with a diameter of 36 inches. Which type of table has the largest area? Square tables Megan loves to plant sunflowers and plans to fill one of the containers below with soil. The dimensions of each container are shown below.

Which container holds the largest amount of soil? Volume of a Rectangular Prism

Volume of a Cylinder

Volume of a Sphere

Container C Coach Kevin brought 18 gallons of water to the football game. How many cups is this equivalent to?

Conversion factor: 1 gallon=16 cups...