Express three root 45 in the form 𝑎 root 𝑏, where 𝑎 and 𝑏 are integers and 𝑏 takes the least possible value.
Before we start, it is worth remembering that integers are whole numbers and also that a surd root 𝑎𝑏 can be written as root 𝑎 multiplied by root 𝑏.
Our first step is to break apart or simplify root 45 as a product of a perfect square and another number. Well, root 45 is the same as root nine multiplied by root five as nine times five is 45. This can be simplified to three root five as the square root of nine is three.
Substituting this information back into our original expression three root 45 gives us three multiplied by three root five. Three multiplied by three is equal to nine. Therefore, the simplified expression is nine root five. Three root 45 written in the form 𝑎 root 𝑏, where 𝑎 and 𝑏 are integers and 𝑏 takes the least possible value, is nine root five.