How do you simplify sqrt ((50^2)-4(13+y))√(502)−4(13+y)?

1 Answer
ceenik
Apr 24, 2017

sqrt((50^2)-4(13+y))=2 sqrt(612-y)√(502)−4(13+y)=2√612−y

Explanation:

sqrt((50^2)-4(13+y))√(502)−4(13+y)

Order of operations.
Exponents first. color(red)((50^2))(502)

sqrt(2500-4(13+y))√2500−4(13+y)

Next we multiply. color(red)(-4(13+y))−4(13+y)

sqrt(2500-52-4y)√2500−52−4y

Add or Subtract common variables. color(red)(2500-52)2500−52

sqrt(2448-4y)√2448−4y

Take out common factor 4. This is convenient since 4 has a perfect square root. Whenever you are trying to simplify a square root always look for factors in your numbers like 4, 9, 16, etc... anything with a perfect square root.

sqrt(color(red)(4)(612-y))√4(612−y)

Complete the square root of 4 and place it outside of the square root.

color(red) "The 2 is now multiplying the square root."The 2 is now multiplying the square root.
color(red)((2)) (sqrt(612-y))(2)(√612−y)

So,
2 sqrt(612-y)2√612−y

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