Find The Square Root Of 24336 By Prime Factorization

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Find the square root of 24336 by prime factorization.

A whole number with a square root that is also a whole number is called a perfect square. Thew following steps will be useful to find square root of a number by prime factorization. Prime factorization by trial division. Https bit ly exponentsandpowersg8 in this video we will learn.

We have to find the square root of above number by prime factorization method. The only square root of zero is zero. So 49 x 2 x 2 x 2 x 2 x 2 x 2 49 x 4 x 4 x 4 3136. Ii inside the square root for every two same numbers multiplied one number can be taken out of the square root.

Square root by prime factorization method example 1 find the square root. Say you want to find the prime factors of 100 using trial division. The product obtained in step v is the required square root. 98 49 x 2.

Now a and b can t be both greater than the square root of n since then the product a b would be greater than sqrt n sqrt n n. So in any factorization of n at least one of the factors must be smaller than the square root of n and if we can t find any factors less than or equal to the square root n must be a prime. Since the number is a perfect square you will be able to make an exact number of pairs of prime factors. 3136 1568 x 2.

Iii combine the like square root terms using mathematical operations. The square root of 8100 is 90. Hence the square root of 8100 is 90. Start by testing each integer to see if and how often it divides 100 and the subsequent quotients evenly.

For example 4 has two square roots. The square root radical is simplified or in its simplest form only when the radicand has no square factors left. Take one factor from each pair. Given the number 8100.

Find the product of factors obtained in step iv. 196 98 x 2. Find primes by trial division and use primes to create a prime factors tree. I decompose the number inside the square root into prime factors.

392 196 x 2. 1568 784 x 2. The prime factors of 8100 is. To learn more about squares and square roots enrol in our full course now.