Winter Holiday Homework---- Radical Expression #2

The given expression is in the form (a + b)^2 - (a - b)^2. Therefore the resulting answer will be in the form 4ab. Therefore the value of it is 4(sqrt(2) + 4)(5),which results in 108.3.(approx)

We are given that $x = \sqrt2 + 4$

Substituting $x$ into the equation given gives us: $(\sqrt2 + 9)^2-(\sqrt2 -1)^2$ Which, by expanding the brackets, gives us: $(83+18\sqrt2) - (3-2\sqrt2)$ Simplifying by collecting alike terms: $80 + 20\sqrt2$ Which can be either put into a calculator, or worked out manually using the approximation: $\sqrt { 2 } \approx 1.414$

$80 + 20\times 1.414$

$= 80 + 28.28$

$= 108.28$

$=\boxed{108.3}$ correct to 1 decimal place, as requested.