Question

1. 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 number.explain with solution plZ​

Answer 1

Answer:

Let us prime factorize 1008. ∴ 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. Now, let's find the square root of 7056 through prime factorization method

Answer 2

$\huge{\mathcal{\underline{\green{ANSWER}}}}$

Let us prime factorize 1008.

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.

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