Question

$$\sqrt{ { 313 }^{ 2 } - { 312 }^{ 2 } }$$

Answer

25

Solution


Simplify  \({313}^{2}\)  to  \(97969\).
\[\sqrt{97969-{312}^{2}}\]
Simplify  \({312}^{2}\)  to  \(97344\).
\[\sqrt{97969-97344}\]
Simplify  \(97969-97344\)  to  \(625\).
\[\sqrt{625}\]
Since \(25\times 25=625\), the square root of \(625\) is \(25\).
\[25\]