Question

Find the square root of:

$73-12\sqrt{35}$

• A. $\sqrt{25}-\sqrt{18}$
• B. $\sqrt{35}-\sqrt{28}$
• C. $\sqrt{45}-\sqrt{18}$
• D. $\sqrt{45}-\sqrt{28}$

Answer 1

The correct option is D $\sqrt{45}-\sqrt{28}$

$73-12\sqrt{35}$

$=45+28-2\cdot 6\cdot \sqrt{35}$

$=45+28-2\sqrt{36\cdot 35}$

$=45+28-2\sqrt{1260}$

$=(\sqrt{45}{)}^2+(\sqrt{28}{)}^2-2\sqrt{45}\times \sqrt{28}$

$=(\sqrt{45}-\sqrt{28}{)}^2$.........................Using $(a-b{)}^2=a^2+b^2-2ab$

$\therefore 73-12\sqrt{35}=(\sqrt{45}-\sqrt{28}{)}^2$

So, the square root of $(73-12\sqrt{35})$ is $(\sqrt{45}-\sqrt{28})$