[tex]$7=r^{\frac{1}{2}}$[/tex]
Answer (2)
We have the equation 7 = r 2 1 .
To solve for r , square both sides of the equation: ( 7 ) 2 = ( r 2 1 ) 2 .
Simplify to find r = 49 .
The solution is 49 .
Explanation
Understanding the Problem We are given the equation 7 = r 2 1 and we want to solve for r .
Raising Both Sides to the Power of 2 To isolate r , we need to eliminate the exponent 2 1 . We can do this by raising both sides of the equation to the power of 2. This gives us ( 7 ) 2 = ( r 2 1 ) 2 .
Simplifying the Equation Simplifying the equation, we have 49 = r . Therefore, r = 49 .
Examples
Imagine you are designing a square garden and you know the length of the fence needed for one side. If the length of the fence is related to the area by the equation s i d e = a re a , and you know the side length is 7 meters, you can find the area by solving 7 = a re a . Squaring both sides gives you the area: a re a = 7 2 = 49 square meters. This shows how solving equations with exponents can help in practical design problems.
To solve the equation 7 = r 2 1 , we square both sides to eliminate the square root, which gives us 49 = r . Thus, the solution is r = 49 .
;
