Simply the following: -3\sqrt{50a^(2) b^(2) }

Question

Simply the following:
`-3\sqrt{50a^(2) b^(2) }`

Answer 1

Given:

The expression is

`-3√(50a^2b^2)`

To find:

The simplified form of the given expression.

Solution:

We have,

`-3√(50a^2b^2)`

It can be written as

`=-3√(2* 25a^2b^2)`

`=-3√(2* 5^2a^2b^2)`

Using the properties of radical and logarithm, we get

`=-3√(2* (5ab)^2)`
`[\because (mn)^x=m^xn^x]`

`=-3√(2)* √((5ab)^2)`
`[\because √(mn)=√(m)√(n)]`

`=-3√(2)* 5ab`

`=-15√(2)ab`

Therefore the simplified form of the given expression is
`-15√(2)ab`.