Question

Simplify with steps7√3 + 10√108

Answer 1

We need to use the following property of radicals to solve this question:

`√(a\cdot b)=√(a)√(b)`

The expression given is:

`7√(3)+10√(108)`

If we want to simplify, we need to rewrite the second term in terms of sqrt(3). We know that 108 is divisible by 3 because the sum of its digits is also divisible by 3.

Then:

`(108)/(3)=36`

We can rewrite:

`7√(3)+10√(108)=7√(3)+10√(36\cdot3)`

Using the property above:

`7√(3)+10√(36)√(3)=7√(3)+10\cdot6√(3)`

Now, we can simplify:

`7√(3)+60√(3)=67√(3)`

Thus, the answer is:

`7√(3)+10√(108)=67√(3)`