Question

Multiply and simplify if possible - radical functions. Thank you!

Answer 1

We want to simplify the following expression

`√(7x)(√(x)+7√(7))`

First, we can apply the distributive rule to rewrite this product

`√(7x)(√(x)+7√(7))=(√(7x))(√(x))+(√(7x))(7√(7))`

Then, using the following property

`√(x)\cdot√(y)=√(x\cdot y)`

we can rewrite our expression as

`(√(7x))(√(x))+(√(7x))(7√(7))=√(7x\cdot x)+7√(7x\cdot7)`

We can remove the squared terms out of the root

`√(7x\cdot x)+7√(7x\cdot7)=x√(7)+7\cdot7√(x)=x√(7)+49√(x)`

and this is our answer.

`√(7x)(√(x)+7√(7))=x√(7)+49√(x)`