Say if these numbers make a right triangle and a Pythagorean triple: 2, 2 square root 2, and 2 square root 3.

I am confident that the answer for both parts of the question is no, because when 2 is squared and when 2 square root 2 is squared it is larger than 2 root 3 squared. I am confused because I do not know if 2 square root 2 is bigger than 2 square root 3. Please help!

(2, 2 square root 2, and 2 square root 3)

means
(2, 2√2, 2√3)

Square each number:
(4, 2²×2, 2²×3)
=(4,8,12)

Do these numbers make a Pythagorean triplet?

The answer is 2 square root 13 and at the bottom of the fraction it’s 13

To determine if the given numbers form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's check if the given numbers satisfy this condition:

Using the Pythagorean theorem, we have:

(Length of hypotenuse)^2 = (Length of side 1)^2 + (Length of side 2)^2

(2√2)^2 = 2^2 + (2√3)^2

4(2) = 4 + 4(3)

8 = 4 + 12

8 = 16

As 8 is not equal to 16, it indicates that the given numbers do not form a right triangle.

Therefore, the answer to the first part of the question is no; the given numbers do not make a right triangle.

Regarding the comparison between 2√2 and 2√3, we can simplify the expressions by multiplying both sides by √2:

2√2 * √2 = 2√3 * √2

2√2(√2) = 2√3(√2)

2 * 2 = √2 * √2 * 3

4 = 2√2 * √2

4 = 2 * 2

As 4 is equal to 4, it indicates that the square root of 2 (√2) is equal to the square root of 3 (√3).

Therefore, the answer to the second part of the question is yes; 2√2 is equal to 2√3.

I hope this clears up any confusion you had. Let me know if there is anything else I can assist you with!

To determine if a set of numbers can form a right triangle, we need to check if they satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's check if 2, √2, and √3 satisfy the Pythagorean theorem:

1. Evaluate the squares of each number:
- 2^2 = 4
- (√2)^2 = 2
- (√3)^2 = 3

2. Now, compare the sum of the squares of the two shorter sides (4 + 2) to the square of the longer side (3).

4 + 2 = 6
(√3)^2 = 3

Since 6 ≠ 3, the numbers 2, √2, and √3 do not satisfy the Pythagorean theorem and therefore cannot form a right triangle.

Regarding your question about whether 2√2 is bigger than 2√3, we can compare them:

1. Simplify the radicals:
- 2√2 cannot be simplified further.
- 2√3 cannot be simplified further either.

2. Now, we can compare the two expressions.

Since √3 ≈ 1.73 and √2 ≈ 1.41, we can do the following comparison:
2 * 1.41 ≈ 2.82
2 * 1.73 ≈ 3.46

Since 2√3 is approximately 3.46, which is greater than 2√2 ≈ 2.82, we can conclude that 2√3 is indeed bigger than 2√2.

In summary, the numbers 2, √2, and √3 do not form a right triangle, and 2√3 is greater than 2√2.