Question

Find the smallest whole number by which 1008 should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.

Answer 1

Let us prime factorize 1008.

$\begin{array}{r | l} 2 & 1008 \\ \cline{2-2} 2 & 504 \\ \cline{2-2} 2 & 252 \\ \cline{2-2} 2 & 126 \\\cline{2-2} 3 & 63 \\\cline{2-2} 3 & 21 \\\cline{2-2} & 7 \\ \end{array}$

1008 = 2×2×2×2×3×3×7

When the prime numbers of 1008 is paired ⇒ (2×2)×(2×2)×(3×3)×7

∴ 7 doesn't have a pair.

∴ The smallest whole number is 7 which needs to be multiply by 1008 to make it a perfect square.

The new number would be ⇒ 1008 × 7 = 7056

Now, let's find the square root of 7056 through prime factorization method.

$\begin{array}{r | l} 7 & 7056 \\\cline{2-2} 2 & 1008 \\ \cline{2-2} 2 & 504 \\ \cline{2-2} 2 & 252 \\ \cline{2-2} 2 & 126 \\\cline{2-2} 3 & 63 \\\cline{2-2} 3 & 21 \\\cline{2-2} & 7 \\ \end{array}$

7056 = 2×2×2×2×3×3×7×7

 When the prime numbers of 7056 is paired ⇒(2×2)×(2×2)×(3×3)×(7×7)

∴ √7056 = 2×2×3×7 = 84

∴ 84² = 7056

Answer 2

.

Step-by-step explanation:

The smallest whole number is 7 which needs to be multiply by 1008 to make it a perfect square.