The correct option is
D √3+√2Given, √3√125+√24.
⇒√3√125+√24=√5+√24
Let square root of 5+√24 be √a+√b.
Then we can write,
⇒5+√24=(√a+√b)2=a+b+2√ab.
Comparing both sides,
⇒a+b=5......(1)
⇒√24=2√ab
Squaring both sides,
⇒24=4ab
⇒6=ab
⇒6=a(5−a)
⇒6=5a−a2
⇒a2−5a+6=0
⇒a2−3a−2a+6=0
⇒a(a−3)−2(a−3)=0
⇒(a−2)(a−3)=0
⇒a=3,2
⇒ for a=3,b=5−a=5−3=2
⇒∴√a+√b=√3+√2
for a=2,b=3
∴√a+√b=√2+√3
∴√5+√24=√2+√3.