Question

How do you solve `\sqrt{k+7}=3\sqrt{2}`?

Answer 1

`k=11`

Explanation:

`sqrt(k+7) = 3sqrt2`
`(sqrt(k+7))^2 = (3sqrt2)^2`
Using exponential properties:
`((k+7)^(1/2))^2 = (3^2)(2^(1/2))^2`
`(k+7)^(1/2X 2) = 9(2^(1/2X2))`
`K+7 = 9 x 2`
`k+7 = 18`
`k=18-7`
`k=11`
Checking the answer:
`sqrt(11+7) = sqrt18`
`sqrt18= sqrt(9X2)`
`sqrt9 X sqrt2`
`3sqrt2`

Answer 2

`k=11`

Explanation:

`"note that "sqrtaxxsqrta=(sqrta)^2=a`

`color(blue)"square both sides"`

`(sqrt(k+7))^2=(3sqrt2)^2`

`rArrk+7=18larrcolor(blue)"subtract 7 from both sides"`

`rArrk=11`

`color(blue)"As a check"`

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

`sqrt(11+7)=sqrt18=sqrt(9xx2)=sqrt9xxsqrt2=3sqrt2`

`rArrk=11" is the solution"`