Question

pls answer it now quite urgent​

Answer 1

Hey there!!

Answer:

By 13.

Therefore, 2925 must be divided by 13 to be a perfect square.

Step-by-step explanation:

• We are given a number 2925. We have to find the number by which 2925 must be divided to obtain a perfect square.

• Firstly, prime factorize 2925.

• 2925 is an odd number so it is not divisible by 2. So start from the next prime which is 3.

• 2925 can be written as three times 975.

       2925=3×975

• 975 can be written as three times 325.

        2925=3×3×325

• 325 can be written five times 65

       2925=3×3×5×65

• 65 can be written as five times 13.

• 2925=3×3×5×5×132925=32×52×131

• In the result, the exponent of 3 is 2 (even), the exponent of 5 is 2 (even) but the exponent of 13 is 1 which is odd. For a number to be a perfect square the primes in its prime factorization should have even exponents. So eliminate 13.

• Therefore, 2925 must be divided by 13 to be a perfect square.

• The perfect square will be 32×52=9×25=225

• Now, find the square root of 225.

• 225=32×52225−−−√=32×52−−−−−−√=3×5=15

• 15 is the square root of 225.

• 2925 must be divided by 13 to obtain a perfect square 225 and the square root of 225 is 15.

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