Question

Find the square root of:

$21-\sqrt{440}$

• A. $\sqrt{12}-\sqrt{10}$
• B. $\sqrt{11}-\sqrt{6}$
• C. $\sqrt{11}-\sqrt{10}$
• D. $\sqrt{10}-\sqrt{2}$

Answer 1

The correct option is C $\sqrt{11}-\sqrt{10}$

$21-\sqrt{440}$

$=11+10-2\sqrt{110}$

$=(\sqrt{11}{)}^2+(\sqrt{10}{)}^2-2\sqrt{110}$

$=(\sqrt{11}-\sqrt{10}{)}^2$................Using $(a-b{)}^2=a^2+b^2-2ab$

$21-\sqrt{440}=(\sqrt{11}-\sqrt{10}{)}^2$

$\therefore \sqrt{21-\sqrt{440}}=\sqrt{11}-\sqrt{10}$
so, the square root of $(21-\sqrt{440})$ is $\sqrt{11}-\sqrt{10}$