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Math: Pre-K - 8th grade; Pre-K through grade 2 (Khan Kids) Early math review; 2nd grade; 3rd grade; 4th grade; 5th grade; 6th grade; 7th grade; 8th grade; 3rd grade math (Illustrative Math-aligned)
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We can simplify the √(1/200) by finding perfect squares that are factors of 200. We could either look directly for the largest perfect square factor or break 200 into smaller factors and find repeated factors. If we have √2 in the denominator, we can multiply by √2/√2 to make an equivalent fraction.
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When simplifying square roots, you need to find perfect square factors and take their square root. You leave any factors inside the radical that are not perfect squares. Yes, you can start by dividing 40 by 2, but 2 is not a perfect square.
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A worked example of simplifying elaborate expressions that contain radicals with two variables. In this example, we simplify √(60x²y)/√(48x).
This works because the square root of any value to the second power is the value, such as: sqrt(y^2) is just y. So we can take a y^2 out of the y^3, and we will have one y left under the square root sign. I hope this helps as well! Here are two examples if you want to do them: sqrt(y^5) sqrt(x^3 y^2)