Question

Which of the following equals 20?

• A. (√8+√2)-4√16
• B. (√9+√11)²
• C. (√6+√4)²+2√24
• D. (√13+√7)²-2√91

Answer 1

Answer:

D. (√13+√7)²-2√91

The correct answer is:

[
(\sqrt{13}+\sqrt{7})^2-2\sqrt{91}
]

Here's why:

1. $((\sqrt{8}+\sqrt{2})-4\sqrt{16})$

=$2\sqrt{2}+\sqrt{2}-4(4)$
=$3\sqrt{2}-16\neq 20$

2. $((\sqrt{9}+\sqrt{11})^2)$

$=(3+\sqrt{11})^2$
$=9+11+6\sqrt{11}$
$=20+6\sqrt{11}\neq 20$

3. $((\sqrt{6}+\sqrt{4})^2+2\sqrt{24})$

Since $(\sqrt{4}=2) and (\sqrt{24}=2\sqrt{6}),$

$(\sqrt{6}+2)^2+2(2\sqrt{6})$
$=6+4+4\sqrt{6}+4\sqrt{6}$
$=10+8\sqrt{6}\neq 20$

$((\sqrt{13}+\sqrt{7})^2-2\sqrt{91})$

Using $((a+b)^2=a^2+b^2+2ab),$

$=13+7+2\sqrt{13\cdot7}-2\sqrt{91}$
$=20+2\sqrt{91}-2\sqrt{91}$
=20

Answer: $(\boxed{(\sqrt{13}+\sqrt{7})^2-2\sqrt{91}})$