Question

Simplify the expression and solve the equation. Show all calculations

Answer 1

First of all, we can observe that

`√(18) = √(2\cdot 9)=√(2)\cdot√(9)=3√(2)`

Then, we can rationalize the denominator by using the formula

`(a-b)(a+b)=a^2-b^2`

If we multiply both numerator and denominator by [/tex]\sqrt{8}+3[/tex] we have

`(3√(2))/(√(8)-3)\cdot(√(8)+3)/(√(8)+3)=(3√(2)(√(8)+3))/(-1) = -3√(2)(√(8)+3)`

We can also observe that

`√(8) = √(2\cdot 4)=√(2)\cdot√(4)=2√(2)`

And the expression simplifies into

`-3√(2)(2√(2)+3) =-12-9√(2) = -3(4+3√(2))`