Question

Solve the following quadratic equations by extracting square roots.Answer the questions that follow.

1. x²=16
2. t²=81
3. r²=100=0
4. x²-144=0
5. 2s²=50

Answer 1

`1.+4,-4\\2. +9,-9\\3. +10,-10\\4. +12, -12\\5. +5, -5`

Explanation:

IN order to solve the quadratic equations you just have to solve the square root of the numeric part of the equation:

`x^(2) =16\\x=√(16)\\ x= +4, -4`

`t^(2) =16\\t=√(81)\\ x= +9, -9`

`r^(2) =100\\r=√(100)\\ x= +10, -10`

`x^(2) -144=0\\x=√(144)\\ x= +12, -12`

`2s^(2)=50\\s^(2)=(50)/(2) \\s=√(25)\\ s= +5, -5`

Just remember that the solution for any square root will always be a negative and a positive number.

Answer 2

1. x=±4

2. t=±9

3. r=±10

4. x=±12

5. s=±5

Explanation:

1. x^2 = 16

Taking square root on both sides

`√(x^2)=√(16)\\√(x^2)=√((4)^2)\\`

x=±4

2. t^2=81

Taking square root on both sides

`√(t^2)=√(81)\\√(t^2)=√((9)^2)`

t=±9

3. r^2-100=0

`r^(2)-100=0\\r^2 =100\\Taking\ Square\ root\ on\ both\ sides\\√(r^2)=√(100)\\√(r^2)=√((10)^2)`

r=±10

4. x²-144=0

x²=144

Taking square root on both sides

`√(x^2)=√(144)\\√(x^2)=√((12)^2)`

x=±12

5. 2s²=50

`(2s^2)/(2) =(50)/(2)\\s^2=25\\Taking\ Square\ root\ on\ both\ sides\\√(s^2)=√(25)\\√(s^2)=√((5)^2)`

s=±5 ..