Question

The square root of $71\times 72\times 73\times 74+1$ is :

• A. 9,375
• B. 9,625
• C. 5,625
• D. 5,255

Answer 1

The correct option is D 5,255

$\text{Here. consider the fact that the product of 4 consecutive numbers + 1 is perfect square.}$
$So,letx=71$
⇒ $\left(71\right)\ast \left(72\right)\ast \left(73\right)\ast \left(74\right)+1=x(x+1)(x+2)(x+3)+1$
⇒$(x²+3x)(x²+3x+2)+1$
⇒$(x²+3x)²+2(x²+3x)+1$
⇒ $(x²+3x+1{)}^2$
⇒ $Squarerootof(x²+3x+1)²=x²+3x+1$
$Here,x=71$
$Therefore,squarerootis=\left(71\right)²+(3\ast 71)+1$
⇒ $5041+213+1$
= $5255$