Math

QuestionCalculate 1.834+π2\frac{1.8^{3}}{\sqrt{4+\pi}-2} and round your answer to the nearest thousandth.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 1.834+π\frac{1.8^{3}}{\sqrt{4+\pi}-} . We need to find the approximate value of this expression, rounded to the nearest thousandth.

STEP 2

First, we need to calculate the value of 1.81.8^{}.
1.81.8^{}

STEP 3

Calculate the value of 1.831.8^{3}.
1.83=5.8321.8^{3} =5.832

STEP 4

Next, we need to calculate the value of 4+π\sqrt{4+\pi}.
4+π\sqrt{4+\pi}

STEP 5

Calculate the value of 4+π\sqrt{4+\pi}.
4+π=3.141\sqrt{4+\pi} =3.141

STEP 6

Now, we need to calculate the value of 4+π2\sqrt{4+\pi}-2.
4+π2\sqrt{4+\pi}-2

STEP 7

Calculate the value of 4+π2\sqrt{4+\pi}-2.
4+π2=1.1416\sqrt{4+\pi}-2 =1.1416

STEP 8

Now that we have the values of the numerator and the denominator, we can divide them to find the value of the given expression.
1.834+π2=5.8321.1416\frac{1.8^{3}}{\sqrt{4+\pi}-2} = \frac{5.832}{1.1416}

STEP 9

Calculate the value of the given expression.
.834+π2=5.832.1416=5.108\frac{.8^{3}}{\sqrt{4+\pi}-2} = \frac{5.832}{.1416} =5.108The approximate value of the given expression, rounded to the nearest thousandth, is5.108.

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