# 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 = 5m^{2}, what is the exact length of one side of the square?

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 = L^{2}

Therefore 5m^{2} = L^{2}

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`

# 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 = 5m^{2}, what is the exact length of one side of the square?

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 = L^{2}

Therefore 5m^{2} = L^{2}

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`