Answer:
[tex]x=2\sqrt{6}[/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
a and b are the legs and c is the hypotenuse. Insert the values:
[tex]\sqrt{10}^2+\sqrt{14}^2=x^2[/tex]
Simplify exponents using the rule [tex]\sqrt{x}^2=x[/tex] :
[tex]10+14=x^2[/tex]
Simplify addition:
[tex]24=x^2\\x^2=24[/tex]
Find the square root:
[tex]\sqrt{x^2}=\sqrt{24}\\ x=\sqrt{24}[/tex]
Simplify in radical form: Find a common factor of 24 that is a perfect square:
[tex]\sqrt{24}=\sqrt{4*6}[/tex]
Separate:
[tex]\sqrt{4}*\sqrt{6}[/tex]
Simplify:
[tex]2*\sqrt{6}\\x=2\sqrt{6}[/tex]
Finito.
