Here's the question you clicked on:
gabriell
√(512)k^(2)
\[\sqrt{a^1} = a^\frac{ 1 }{ 2 }\] now, in your example, you have: \[\sqrt{a^2} = a^\frac{ 2 }{ 2 } \] and you know: \[\frac{ 2 }{ 2 } = 1\]. And when you have \[\sqrt{4} = \sqrt{ 2 \times 2} = 2\] Similarly: \[\sqrt{100} = \sqrt{20 \times 5 } = \sqrt{(5 \times 4) \times 5} = \sqrt{(5 \times (2 \times 2)) \times 5} = \sqrt{(5 \times 5) (2 \times 2)}\] hence: \[\sqrt{(5 \times 5) (2 \times 2)} = 5 \times 2 = 10\]
If you notice the patter, I am taking each pair of 5 and pair of 2 out of the radical. But only took out ONE PAIR of 5's and ONE PAIR of 2's. If you have more than one pair of 2's, then you would take out a 4. Because you know 2 x 2 = 4. and if you have two PAIRS of 5's you would take out a 25. Since you should know that 5 x 5 = 25.