CCA Unit 4 Lesson 11

3.
If a number is not a rational number, then it is ______.

~ an integer
~ and irrational number***
~ a whole number
~ a radical

4.
James attached a diagonal brace across a rectangular frame that measures 6 feet by 8 feet. What is the length of the diagonal brace?

~ 2 feet
~ 10 feet
~ 14 feet
~ 48 feet***

5.
Which number is a perfect cube?

~ 3
~ 15***
~ 64
~ 567

6.
When adding the square root of 16 and -8, which type of number is the sum?

~ integer
~ irrational number***
~ radical
~ whole number

Please check my answers.
Thank You!
:)

4.

James attached a diagonal brace across a rectangular frame that measures 6 feet by 8 feet. What is the length of the diagonal brace?

~ 2 feet
~ 10 feet
~ 14 feet
~ 48 feet***
===================
36+64 = 100
sqrt(100) = 10

Could someone just gie me the answers... please

give*

Thanks!

So what is 5, c?

4. To find the length of the diagonal brace for a rectangular frame, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the two sides are the length and width of the rectangular frame.

Using the Pythagorean theorem, you can calculate the length of the diagonal brace as follows:
a^2 + b^2 = c^2

where a = 6 feet (length of the rectangle)
b = 8 feet (width of the rectangle)
c = diagonal brace (unknown)

Substituting the values:
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2

To solve for c, you take the square root of both sides:
√100 = √c^2
10 = c

Therefore, the length of the diagonal brace is 10 feet.

5. To determine which number is a perfect cube, you need to find the cube root of each option.

The cube root of a number is the value that, when cubed, results in the original number. For example, the cube root of 27 is 3, because 3^3 = 27.

Checking each option:
Cube root of 3: ∛3 ≈ 1.44 (not a whole number)
Cube root of 15: ∛15 ≈ 2.466 (not a whole number)
Cube root of 64: ∛64 = 4 (a whole number)
Cube root of 567: ∛567 ≈ 8.009 (not a whole number)

Therefore, the only number that is a perfect cube is 64.

6. To add the square root of 16 and -8, you can simplify each term separately and then perform the addition.

√16 = 4 (since 4^2 = 16)
√(-8) = √(-1 * 8) = i√8 (where i is the imaginary unit)

Note: The square root of a negative number is not a real number, but an imaginary number. In this case, we have √(-8), which simplifies to i√8.

Now, we add the two terms:
√16 + √(-8) = 4 + i√8

The sum, 4 + i√8, is an irrational number, as it contains both a real number (4) and an imaginary number (i√8).