We are asked to simplify the following expression
[tex]\sqrt[]{\frac{405}{324}}[/tex]
Recall the quotient rule of radicands given by
[tex]\sqrt[]{\frac{a}{b}}=\frac{\sqrt[]{a}}{\sqrt[]{b}}[/tex]
Applying the above rule to the given expression
[tex]\sqrt[]{\frac{405}{324}}=\frac{\sqrt[]{405}}{\sqrt[]{324}}[/tex]
Notice that the square root of 324 is equal to 18
[tex]\frac{\sqrt[]{405}}{\sqrt[]{324}}=\frac{\sqrt[]{405}}{18}[/tex]
Also, notice that we can break 405 into factors as
[tex]\sqrt[]{405}=\sqrt[]{81\times5}=\sqrt[]{81}\cdot\sqrt[]{5}=9\cdot\sqrt[]{5}[/tex]
So, the expression becomes
[tex]\frac{\sqrt[]{405}}{18}=\frac{9\cdot\sqrt[]{5}}{18}=\frac{\sqrt[]{5}}{2}[/tex]
Therefore, the simplified expression is
[tex]\frac{\sqrt[]{5}}{2}[/tex]
a = √5
b = 2
