It says to use the Pythagorean theorem to solve each one. The theorem is a^2 + b^2 = c^2. We can plug in the values for each one and solve the equation to find the missing value.
1.
4² + 7² = c²
16 + 49 = c²
65 = c²
√65 = c
2.
3² + b² = 7²
9 + b² = 49
b² = 40
b = √40
b = √(4*10)
b = √4 * √10
b = 2√10
3.
3² + 5² = c²
9 + 25 = c²
34 = c²
√34 = c
4.
2² + 9² = c²
4 + 81 = c²
85 = c²
√85 = c
5.
4² + b² = 9²
16 + b² = 81
b² = 65
b = √65
6.
3² + 3² = c²
9 + 9 = c²
18 = c²
√18 = c
√(9*2) = c
√9 * √2 = c
3√2 = c
7.
4² + 4² = c²
16 + 16 = c²
32 = c²
√32 = c
√(16*2) = c
√16 * √2 = c
4√2 = c
8.
a² + 4² = 8²
a² + 16 = 64
a² = 48
a = √48
a = √(16*3)
a = √16 * √3
a = 4√3
