Question

What is the value of:(√18 + √2)²-(√8 + √2)²

• A. 14
• B. 15
• C. 16
• D. 17

Answer 1

Answer:

A. 14

We need to find:

$(\sqrt{18}+\sqrt{2})^2-(\sqrt{8}+\sqrt{2})^2$

Step 1: Simplify the square roots

$\sqrt{18}=3\sqrt{2}, \qquad \sqrt{8}=2\sqrt{2}$

So,

$(3\sqrt{2}+\sqrt{2})^2-(2\sqrt{2}+\sqrt{2})^2$
$=(4\sqrt{2})^2-(3\sqrt{2})^2$

Step 2: Square each term

$(4\sqrt{2})^2=16\times2=32$
$(3\sqrt{2})^2=9\times2=18$

Subtract

32-18=14

$Answer: (\boxed{14})$