Question

In the right triangle, AC = BC = 2. What is AB?

Answer 1

Formula for hypotenuse:

`\sqrt{ a^(2) + b^(2) }=c`

a would be AC
b would be CB
c is AB


`\sqrt{ 2^(2) +2^(2) }`

`√(4+4)`

`√(8)`

It is
`√(8)` or
`2√(2)` or about 2.83

Answer 2

Short Answer: x = 2*sqrt(2)
The Pythagorean Theorem states that
a^2 + b^2 = c^2

Givens
a = 2
b = 2
c = ???

Sub and solve
2^2 + 2^2 = c^2
c^2 = 4 + 4
c^2 = 8 Take the sqrt of both sides of the equation
sqrt(c^2) = sqrt(8) Express 8 in it's prime factor form.
sqrt(c^2) = sqrt(2 * 2 * 2)

The rule about square roots is
If you have a pair of prime factors under the root sign, you take out one of the prime factors and throw the other one away.

sqrt(c^2) = 2*sqr(2)

Answer x = 2*sqrt(2)