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Tucker Powell
09/11/2023 · High School

smallest oumber by which 2450 be multiplied so that become a perfect square

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To find the smallest number by which 2450 must be multiplied to become a perfect square, we first need to factor 2450 into its prime factors. 1. **Factor 2450**: - Divide by 2: \( 2450 \div 2 = 1225 \) - Divide by 5: \( 1225 \div 5 = 245 \) - Divide by 5 again: \( 245 \div 5 = 49 \) - Divide by 7: \( 49 \div 7 = 7 \) - Divide by 7 again: \( 7 \div 7 = 1 \) So, the prime factorization of 2450 is: \[ 2450 = 2^1 \times 5^2 \times 7^2 \] 2. **Identify the exponents**: - The exponent of 2 is 1 (which is odd). - The exponent of 5 is 2 (which is even). - The exponent of 7 is 2 (which is even). 3. **Make the exponents even**: - For the factor of 2, we need to multiply by \( 2^1 \) to make the exponent even (1 becomes 2). - The factors of 5 and 7 are already even, so we do not need to multiply by anything for those. 4. **Calculate the smallest number**: - The smallest number we need to multiply by is \( 2^1 = 2 \). Thus, the smallest number by which 2450 must be multiplied to become a perfect square is **2**.

Quick Answer

The smallest number is 2.
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