Given:
The expression is
[tex]-3\sqrt{50a^2b^2}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]-3\sqrt{50a^2b^2}[/tex]
It can be written as
[tex]=-3\sqrt{2\times 25a^2b^2}[/tex]
[tex]=-3\sqrt{2\times 5^2a^2b^2}[/tex]
Using the properties of radical and logarithm, we get
[tex]=-3\sqrt{2\times (5ab)^2}[/tex] [tex][\because (mn)^x=m^xn^x][/tex]
[tex]=-3\sqrt{2}\times \sqrt{(5ab)^2}[/tex] [tex][\because \sqrt{mn}=\sqrt{m}\sqrt{n}][/tex]
[tex]=-3\sqrt{2}\times 5ab[/tex]
[tex]=-15\sqrt{2}ab[/tex]
Therefore the simplified form of the given expression is [tex]-15\sqrt{2}ab[/tex].
