Answer:
a. [tex]\frac{5}{4}[/tex]
b. [tex]\frac{3}{2}[/tex] or [tex]1\frac{1}{2}[/tex]
Steps:
For a.)
- Apply radical rule: [tex]\sqrt[n]{\frac{a}{b} } =\frac{\sqrt[n]{a}}{\sqrt[n]{b} }[/tex], assuming [tex]a\geq 0,b\geq 0[/tex]
- = [tex]\frac{\sqrt{25} }{\sqrt{16} }[/tex]
[tex]\sqrt{16}=4[/tex]
[tex]\frac{\sqrt{25} }{4}[/tex]
[tex]\sqrt{25} =5[/tex]
[tex]=\frac{5}{4}[/tex]
For b.)
- [tex]\frac{\sqrt{18} }{\sqrt{8} }[/tex]
- Apply radical rule: [tex]\frac{\sqrt{a} }{\sqrt{b} } =\sqrt{\frac{a}{b} }[/tex]
- Which means[tex]\frac{\sqrt{18} }{\sqrt{8} }=\sqrt{\frac{18}{8} }[/tex]
[tex]=\sqrt{\frac{18}{8} }[/tex]
2. Cancel [tex]\frac{18}{8}[/tex]: [tex]\frac{9}{4}[/tex]
= [tex]\sqrt{\frac{9}{4} }[/tex]
Now apply the radical rule: [tex]\sqrt[n]{\frac{a}{b} } =\frac{\sqrt[n]{a} }{\sqrt[n]{b} }[/tex] assuming [tex]a\geq 0,b\geq 0[/tex]
- = [tex]\frac{\sqrt{9} }{\sqrt{4} }[/tex]
[tex]\sqrt{4}=2[/tex]
[tex]=\frac{\sqrt{9} }{2}[/tex]
[tex]\sqrt{9}=3[/tex]
The final answer for b.) should be [tex]\frac{3}{2}[/tex]
