Solving radicals and quadratic equations with square roots
√0=
0
√1=
1
BEFORE solving the equation √x=7 for x, how many solutions would you expect?
1 solution
√100=
10
√121=
11
√144=
12
√169=
13
√196=
14
√225=
15
√4=
2
BEFORE solving the equation 5x²=125 for x, how many solutions would you expect?
2 solutions, a positive and negative answer
BEFORE solving the equation x²=9 for x, how many solutions would you expect?
2 solutions, a positive and negative answer
√9=
3
√16=
4
√25=
5
√36=
6
√49=
7
√64=
8
√81=
9
Solve for x: √x = 9
SQUARE both sides (not square root!) x = 81
Solve for x: √x = 7
SQUARE both sides! x = 49
Solve for x: x² = 9
Square ROOT both sides! x = ±3
Solve for x: 6x² = 600
divide by 6, square toot both sides x = ±10
Solve for x: 5x² = 125
divide by five, then square root! x = ±5
Solve for x: √x +3 = 19
Subtract 3 then SQUARE both sides (not square root!) x = 256
Solve for x: x² + 8 = 89
Subtract 8, Square root both sides! x = ±9
x² = -25
no real solution
(x + 2)² = 16
x = 2 or -6
(x - 1)² = 9
x = 4 or -2
x² + 1 = 26
x = 5 or -5
(x - 3)² = 4
x = 5 or 1
x² - 2 = 34
x = 6 or -6
x² = 49
x = 7 or -7
x² = 64
x = 8 or -8
x² - 5 = 76
x = 9 or -9
(x - 4)² = 12
x = ±√12 + 4
x² = 40
x = ±√40
x² + 5 = 10
x = ±√5