I have three questions.
1 answer:
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Answer:
Step-by-step explanation:
These cannot combine the way they are. The rule for adding and subtracting radicals is really picky. Not only does the index have to be the same (the little number that is sitting outside in the bend of the radical {ours is a 2, which isn't usually there, but is instead understood to be a square root}), but the radicand, the expression under the square root (or cubed root, or fourth root, etc) has to the same as well. All of our radicals are square roots, so that's good, but the radicands are all different. The first one is an 8, the next one is a 72, and the last one is a 50. BUT if we can rewrite them by simplifying them and then the radicands are the same, we're in good shape.
Simplify by taking the prime factorization of each of those numbers.
8: 4*2 and 4 is a perfect square, so we'll stop there
72: 36*2 and 36 is a perfect square, so we'll stop there
50: 25*2 and 25 is a perfect square, so we'll stop there.
Now, rewrite each one of them in terms of their prime factorization:
and then pull out each perfect square as its root:
and now all the radicands are the same, so we can add them to get
or simply
Answer:
The formula for calculating the width of the window is
Step-by-step explanation:
<u><em>The question in English is</em></u>
A rectangular window is l meters wide and h meters high, with a perimeter of 6 meters and an area of 2m². What is the formula for calculating the width of the window?
we know that
The perimeter of the window is equal to
we have
so
simplify
isolate the variable l
----> equation A
The area of the window is equal to
we have
so
----> equation B
substitute equation A in equation B
solve for w
The formula to solve a quadratic equation of the form
is equal to
in this problem we have
so
substitute in the formula
---> formula for calculating the width of the window