Question

$\text{The value of the expression}{p}^2-q^2,\text{if}p=(5+2\sqrt{3})\&q=(5-2\sqrt{3})\text{is}$

• A. $40\sqrt{3}$
• B. $-40\sqrt{3}$
• C. $40$.
• D. $-40$

Answer 1

The correct option is A $40\sqrt{3}$

Given surds:
$p=(5+2\sqrt{3}))$
$q=(5-2\sqrt{3})$

$p+q=(5+2\sqrt{3})+(5-2\sqrt{3})=10$

$p-q=(5+2\sqrt{3})-(5-2\sqrt{3})=4\sqrt{3}$

Note: $p^2-q^2=(p+q)\times (p-q)$

$\text{So,}{p}^2-q^2=(p+q)\times (p-q)$
$=10\times 4\sqrt{3}$
$=40\sqrt{3}$