Answer:
Multiply the entire expression by the radical denominator. This keeps the expression equal and makes the denominator 3, a whole number.
Step-by-step explanation:
The denominator is irrational because it is a radical number, √3.
To rationalize the denominator, multiply the entire expression by √3. The denominator will become a whole number. This works because you multiply top and bottom by the same value.
[tex]\frac{3 + \sqrt{2} }{\sqrt{3}}[/tex]
[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{(\sqrt{3})(\sqrt{3})}[/tex]
[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]
√3 X √3 = 3 because:
√3 X √3 = √3²
Squaring a number and also finding its square root are opposites, or reverse operations. They cancel out
You probably need to simplify the rest of the equation too.
[tex]\frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]
[tex]= \frac{3(\sqrt{3}) + (\sqrt{2})(\sqrt{3})}{3}[/tex] Distribute over brackets
[tex]= \frac{3(\sqrt{3}) + \sqrt{2*3}}{3}[/tex] Simplify
[tex]= \frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex]
Some people use a more simplified version whether they simplify each term in the numerator:
[tex]\frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex] (3√3)÷3 = √3
[tex]\sqrt{3} + \frac{\sqrt{6}}{3}[/tex]
