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Sindrei [870]
3 years ago
7

What is the exact value of the expression the square root of 20. + the square root of 24. - the square root 54.? simplify if pos

sible?
Mathematics
2 answers:
Bumek [7]3 years ago
7 0
.  \sqrt{20}+ \sqrt{24} - \sqrt{54}.  The idea is to simplify the radicand into a perfect square or a multiplication of 2 numbers and 1 of those is a perfect square.  Let's rewrite our simplified radicands: \sqrt{4*5} + \sqrt{4*6}- \sqrt{9*6}.  In the first two, 4 is the perfect square and will be pulled out as a 2, leaving whatever is left under the radical sign, and in the third one, 9 is the perfect square that will be pulled out as a 3.  2 \sqrt{5} +2 \sqrt{6} -3 \sqrt{6}.  The rule for adding and subtracting radicands is that a. the index has to be the same (ours are all square roots, so the indexes are all 2), and b. the radicands have to be like in order to combine them.  Our square root of 6 is in 2 of those, so those can be combined, but not the square root of 5.  Combining like terms now we have 2 \sqrt{5} -1 \sqrt{6}
aksik [14]3 years ago
4 0
\sqrt{20} =  \sqrt{4}  \sqrt{5}  = 2 \sqrt{5}
\sqrt{24} =  \sqrt{4} \sqrt{6} = 2 \sqrt{6}
\sqrt{54} =  \sqrt{9} \sqrt{6} = 3 \sqrt{6}

Because you can only add and subtract radicals with the same radicand,
you get 2\sqrt{5} -  \sqrt{6}
that is the simplified answer but if you want it in decimals, 2.022 is what you get.
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Rainbow [258]

Answer:

The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.

Pi = π = 3.14

Step-by-step explanation:

Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)

The formula for the circumference of circle when Diameter is given = πD

π = Circumference / Diameter

For Circle A :

Circle A has a diameter of 7 inches, a circumference of 21.98 inches.

π = 21.98 inches/7 inches

π = 3.14

For Circle B

The diameter of circle B is 6 inches, the circumference is 18.84 inches

π = 18.84 inches/6 inches

π = 3.14

Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)

The formula for the area of the circle = πr²

Circle A has a diameter of 7 inches, an area of 38.465 square inches.

r = Radius = 7 inches ÷ 2

= 3.5 inches

π = Area / Radius²

π = 38.465 in²/(3.5 inches)²

π = 3.14

For Circle B

The diameter of circle B is 6 inches, and the area is 28.26 square inches.

r = Radius = 6 inches ÷ 2

= 3 inches

π = Area / Radius²

π = 28.26 in²/(3 inches)²

π = 3.14

Part C: What observation can you make about the value of pi for circles A and B? (2 points)

The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.

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german

Answer:

\dfrac{x^4y^4}{81}

Step-by-step explanation:

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Find the volume of the rectangular prism
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Answer:

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Step-by-step explanation:

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3 years ago
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Convert 0.245 into a percent and choose the appropriate result.
pantera1 [17]

Answer:

A. 24.5

Step-by-step explanation:

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Given that (in picture)...
GuDViN [60]
<h3>Answer:  a = -3 and b = 5</h3>

=================================================

Work Shown:

Multiply top and bottom by \sqrt{2} to rationalize the denominator

\frac{10-\sqrt{18}}{\sqrt{2}}\\\\\frac{\sqrt{2}(10-\sqrt{18})}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{2}*10-\sqrt{2}*\sqrt{18}}{\sqrt{2*2}}\\\\\frac{\sqrt{2}*10-\sqrt{2*18}}{\sqrt{4}}\\\\\frac{10\sqrt{2}-\sqrt{36}}{2}\\\\\frac{10\sqrt{2}-6}{2}\\\\\frac{-6+10\sqrt{2}}{2}\\\\\frac{2(-3+5\sqrt{2})}{2}\\\\-3+5\sqrt{2}\\\\

We end up with something in the form a+b\sqrt{2} where a = -3 and b = 5

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