Question

Find the smallest whole number by which 2800 should be divided so as to get a perfect square.

Answer 1

First we need to do the prime factorisation of the given number.

The given number is 2800.

$\begin{array}{r | l} 2 & 2800 \\ \cline{2-2} 2& 1400 \\ \cline{2-2} 2 & 700 \\ \cline{2-2} 2 & 350 \\\cline{2-2} 5& 175 \\\cline{2-2} 5& 35 \\\cline{2-2} 7& 7 \\ \cline{2-2} & 1 \\ \end{array}$

The product of the primes are ⇒ (2×2)×(2×2)×(5×5)×7

∴ 2800 is not a perfect square since 7 doesn't have a pair

∴ 7 should be divided to obtain a perfect square.

Additional Information :)

2800÷7 = 400

The square root of 400 would be ⇒ 2×5×2

∴√400 = 20

Answer 2

Answer:

The product of the primes are ⇒ (2×2)×(2×2)×(5×5)×7

∴ 2800 is not a perfect square since 7 doesn't have a pair

∴ 7 should be divided to obtain a perfect square.  

Additional Information :)

2800÷7 = 400

The square root of 400 would be ⇒ 2×5×2

∴√400 = 20

Step-by-step explanation: