1. The problem is to simplify the square roots given: a) $\sqrt{52}$ and b) $\sqrt{170}$.\n\n2. The formula to simplify square roots is to find the prime factors and take out pairs as single numbers. For example, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$.\n\n3. For a) $\sqrt{52}$, factor 52 into $4 \times 13$.\n\n4. Then, $\sqrt{52} = \sqrt{4 \times 13} = \sqrt{4} \times \sqrt{13} = 2\sqrt{13}$.\n\n5. For b) $\sqrt{170}$, factor 170 into $25 \times 6.8$ is not exact, so try $25 \times 6.8$ is not an integer factorization. Instead, factor 170 as $25 \times 6.8$ is incorrect. Let's try $170 = 2 \times 85$, and $85 = 5 \times 17$. No perfect square factors except 25 is not a factor. So check for perfect squares: 25 is not a factor, 16 no, 9 no, 4 no, 1 yes. So no perfect square factors other than 1.\n\n6. So $\sqrt{170}$ cannot be simplified further and remains $\sqrt{170}$.\n\nFinal answers:\n\na) $2\sqrt{13}$\n\nb) $\sqrt{170}$