Exact answers

If your answer is a surd or $pi$ then you can’t get a more accurate number (as long as they have been simplified).

Exact answer = Surd or $pi$

Examples

1. The area of a square = 5m², what is the exact length of one side of the square?

When measuring a square the answer doesn’t need simplifying

Area of a square = Length x Height

And in this case as length and height are the same

Area of a square = Length x Length

Area of a square = L²

Therefore 5m² = L²

Whatever you do to one side of an equation, you must also do to the other.

So, the square root of both sides.

$sqrt5=sqrt(L^2)$

$sqrt5=L$

Answer: Exact length = $sqrt5$

2. Find the exact area of a circle with radius 5

Area of a circle = $pir^2$

Area of a circle = $pi5^2$

= $pi25$ $m^2$

Answer: Area of a circle = $pi25$ $m^2$