Finding Square Roots

To find the square root of $1156$ using prime factorization, we start by finding its prime factors: $2 \times 2 \times 17 \times 17$. Next, we attempt to divide these prime factors into two identical groups. We can arrange them as $(2 \times$ $) \times (2 \times 17)$. Since we can perfectly split the factors into two equal groups, the product of the factors in either group combines to form the square root. Evaluating this product, we calculate $2 \times 17 = 34$. Therefore, we can confidently state that $\sqrt{1156}$ is .