Since 17 appears twice as a factor, we can express the factorization as 17². This shows that 289 is a perfect square.

Taking the principal square root of both sides, the square root of 17² simplifies directly to 17.

Find the square root 2 8 9

Answer: $17$

Step-by-step solution

Step 1: Prime factorize the number

To find the square root of $289$ , we test for divisibility by prime numbers. The prime numbers $2$ , $3$ , $5$ , $7$ , $11$ , and $13 do$ not divide $289$ . Testing the prime number $17$ , we find that $289 \div 17 = 17$ .

Step 2: Express as a square

Since $17$ appears twice as a factor, we can express the factorization as $17^2$ . This shows that $289$ is a perfect square.

Step 3: Evaluate the square root

Taking the principal square root of both sides, the square root of $17^2$ simplifies directly to $17$ .

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