Question

Find the smallest number by which $9408$ must be divided so that the quotient is a perfect square. Find the square root of the quotient.

• A. Smaller number:$5$ , Quotient: $3036$, Square root: $54$.
  
• B. Smaller number: $3$, Quotient: $3136$, Square root: $56.$
• C. Smaller number:$7,$ Quotient: $3236$, Square root: $57.$
• D. Data insufficient
  

Answer 1

Answer: (B)

Smaller number: $3$, Quotient: $3136$, Square root: $56.$

We have 9408= $\underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{2\times 2}\times 3\times \underset{–}{7\times 7}$
If we divide 9408 by the factor 3 then
$9408÷3=3136=\underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{7\times 7}$ which is a perfect square (because $3136=(56{)}^2$)
And $\sqrt{3136}=2\times 2\times 2\times 7=56$