Question

Find the solution(s) of the following equation.

a2 = 64/225

A: a = 8/15
B: a = -8/15
C: a = sqroot.64/225
D: a = - sqroot.64/225
E: None of the Above

Answer 1

A, B, C, and D are correct.

Explanation:

`\sf a^2 = (64)/(225)`

Taking the square root of both sides:

`\sf √(a^2) = \sqrt{(64)/(225)}`

The square root of a² is simply |a|, since a² can be positive or negative:

`\sf |a| = (8)/(15)`

Now, considering both positive and negative values of a.

`\sf a = (8)/(15) \textsf{ (positive square root) }`

`\sf a = -(8)/(15) \textsf{(negative square root)}`

So, the correct answer is:

• 
  `\sf A: a = (8)/(15)`
• 
  `\sf B: a = -(8)/(15)`
• 
  `\sf C: a = \sqrt{(64)/(225)} = (8)/(15)`
• 
  `\sf D: a = -\sqrt{(64)/(225)} = -(8)/(15)`

So, the options A, B, C, and D are correct.