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melisa1 [442]
2 years ago
12

Simplify completely. √32 A. 8√2 B. 4√2 C. 2√16 D. 4√8

Mathematics
2 answers:
tia_tia [17]2 years ago
7 0
4<span>√<span>2.......is this one of your options

</span></span>
soldier1979 [14.2K]2 years ago
5 0
√32
= √16 .<span>√2
= 4</span><span>√2

answer is </span><span>B. 4√2</span>
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nika2105 [10]
Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.

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There are three right triangles we can work with.

Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation x^{2} + 48^{2} = z^{2}

Triangle with sides 27, x and y. Here y is the hypotenuse so we get 27^{2} + x^{2} = y^{2}

Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get y^{2} + z^{2} = (27+48)^{2}. That is, y^{2} + z^{2} = 5625

We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation: y^{2} + z^{2} = 5625 and replace z^{2} and y^{2} using expressions that contain an expression in terms of x from the first two equations we came up with.

That gives us: 48^{2} + x^{2} + x^{2} + 27^{2} =5625 which we solve for x as follows:

2 x^{2} + 3033 =5625&#10;2x^{2}  =2592&#10; x^{2} =1296&#10;x=36

Now that we know x we can substitute 36 for x into the equation 48^{2} + x^{2} = z^{2} and solve for z as follows:
48^{2} + 36^{2} = z^{2} &#10;2304+1296=z^{2} &#10;3600=z^{2} &#10;z=60

This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
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