Question

$x^2=11+2\sqrt{30}$, find x

• A. zero is a natural number
• B. -1 is a whole number
• C. 6.5 is an integer
• D. All of these

Answer 1

The correct option is D

All of these

Given that $x^2=11+2\sqrt{30}$

Spiliting 11 as 5 + 6, we have

$x^2=5+6+2\sqrt{30}$

$5=\sqrt{(}5{)}^2$ & $6=\sqrt{(}6{)}^2$

$\therefore x^2=\sqrt{(}5{)}^2+\sqrt{(}6{)}^2+2\sqrt{30}$

= $(\sqrt{5}+\sqrt{6}{)}^2$ ( $(a+b{)}^2=a^2+2ab+b^2$)

$x^2=(\sqrt{5}+\sqrt{6}{)}^2$

$x=\sqrt{5}+\sqrt{6}$