Find the smallest number by which each of the following numbers should be multiplied so as to get a perfect square. Also, find the square root of the perfect square thus obtained. a)3072 b)4802 c)1452 d)845

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Factorize 3072: To find the smallest number by which 3072 should be multiplied to get a perfect square, we first factorize 3072 into its prime factors. 3072 = 2^10 * 3Make 3072 a perfect square: To make 3072 a perfect square, we need to have pairs of prime factors. We have an even power of 2, which is good, but we need another 3 to pair up with the existing one. So, we need to multiply 3072 by 3 to get a perfect square. 3072 * 3 = 2^10 * 3^2Square root of 3072: The square root of the perfect square obtained by multiplying 3072 by 3 is: √(2^10 * 3^2) = 2^5 * 3 = 32 * 3 = 96Factorize 4802: Now, we move on to the number 4802. We factorize 4802 into its prime factors. 4802 = 2 * 2401 = 2 * 7^4Make 4802 a perfect square: To make 4802 a perfect square, we need to multiply it by 2 to pair up with the existing 2. 4802 * 2 = 2^2 * 7^4Square root of 4802: The square root of the perfect square obtained by multiplying 4802 by 2 is: √(2^2 * 7^4) = 2 * 7^2 = 2 * 49 = 98Factorize 1452: Next, we consider the number 1452. We factorize 1452 into its prime factors. 1452 = 2^2 * 3 * 11^2Make 1452 a perfect square: To make 1452 a perfect square, we need to multiply it by 3 to pair up with the existing 3. 1452 * 3 = 2^2 * 3^2 * 11^2Square root of 1452: The square root of the perfect square obtained by multiplying 1452 by 3 is: √(2^2 * 3^2 * 11^2) = 2 * 3 * 11 = 6 * 11 = 66Factorize 845: Finally, we look at the number 845. We factorize 845 into its prime factors. 845 = 5 * 13^2Make 845 a perfect square: To make 845 a perfect square, we need to multiply it by 5 to pair up with the existing 5. 845 * 5 = 5^2 * 13^2Square root of 845: The square root of the perfect square obtained by multiplying 845 by 5 is: √(5^2 * 13^2) = 5 * 13 = 65

Find the smallest number by which each of the following numbers should be multiplied so as to get a perfect square. Also, find the square root of the perfect square thus obtained. a) $3072$ b) $4802$ c) $1452$ d) $845$

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Find the smallest number by which each of the following numbers should be multiplied so as to get a perfect square. Also, find the square root of the perfect square thus obtained. a) $3072$ b) $4802$ c) $1452$ d) $845$