Given:
Consider the given expression is:
[tex]\sqrt{12}\cdot \sqrt{18}[/tex]
To find:
The value of the product.
Solution:
We have,
[tex]\sqrt{12}\cdot \sqrt{18}[/tex]
It can be written as:
[tex]=\sqrt{2\times 2\times 3}\cdot \sqrt{2\times 3\times 3}[/tex]
[tex]=\sqrt{2^2\times 3}\cdot \sqrt{2\times 3^2}[/tex]
[tex]=2\sqrt{3}\cdot 3\sqrt{2}[/tex]
On further simplification, we get
[tex]=(2\cdot 3)\sqrt{3}\cdot \sqrt{2}[/tex]
[tex]=6\sqrt{3\cdot 2}[/tex]
[tex]=6\sqrt{6}[/tex]
Therefore, the value of the product is [tex]6\sqrt{6}[/tex].
