[tex]\sqrt{10}[/tex] / 15
using the laws of radicals
• [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
• [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a
the expression can be simplified to
2 / 3[tex]\sqrt{10}[/tex]
However, to fully simplify we must rationalise the denominator
This is achieved by multiplying numerator/ denominator by [tex]\sqrt{10}[/tex]
= 2 / 3[tex]\sqrt{10}[/tex] × [tex]\sqrt{10}[/tex] / [tex]\sqrt{10}[/tex]
= 2[tex]\sqrt{10}[/tex] / 30 = [tex]\sqrt{10}[/tex] / 15 ← in simplest form
