Given:
The expressions are:
[tex]\sqrt[3]{24},\sqrt{48},\sqrt[3]{54},\sqrt{45}[/tex]
To find:
The simplified form of each expression.
Solution:
We have,
[tex]\sqrt[3]{24}[/tex]
It can be written as:
[tex]\sqrt[3]{24}=\sqrt[3]{2\times 2\times 2\times 3}[/tex]
[tex]\sqrt[3]{24}=2\sqrt[3]{3}[/tex]
Similarly,
[tex]\sqrt{48}=\sqrt{2\times 2\times 2\times 2\times 3}[/tex]
[tex]\sqrt{48}=(2\times 2)\sqrt{3}[/tex]
[tex]\sqrt{48}=4\sqrt{3}[/tex]
And,
[tex]\sqrt[3]{54}=\sqrt[3]{2\times 3\times 3\times 3}[/tex]
[tex]\sqrt[3]{54}=3\sqrt[3]{2}[/tex]
In the same way,
[tex]\sqrt{45}=\sqrt{3\times 3\times 5}[/tex]
[tex]\sqrt{45}=3\sqrt{5}[/tex]
Therefore, the required pairs are:
[tex]\sqrt[3]{24}\to 2\sqrt[3]{3}[/tex]
[tex]\sqrt{48}\to 4\sqrt{3}[/tex]
[tex]\sqrt[3]{54}\to 3\sqrt[3]{2}[/tex]
[tex]\sqrt{45}\to 3\sqrt{5}[/tex]
