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2 years ago

Simplify the radical expression by rationalizing the denominator.

Mathematics

1 answer:

artcher [175]2 years ago

4 0

$\frac{4}{\sqrt{21}} = \frac{4}{\sqrt{21}} \times \frac{\sqrt{21}}{\sqrt{21}} =\boxed{ \frac{4\sqrt{21}}{21}}$

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3 years ago

PLS HELP!! GIVING BRAINLIEST TO FIRST CORRECT ANSWER!!+50 POINTS

Elena-2011 [213]

Answer(s):

154 in²
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38.5 m²

Revising the area of a circle formula

We already know that the area of a circle is expressed as $\pi r^{2}$ .

The "r" variable is known as the radius.

<h2><u>Solving each problem given:</u></h2><h3>Solving Problem 4:</h3>

We are given the radius of circle, which is 7 in. Let us substitute the radius in the formula. Once substituted, we can simplify the expression obtained to determine the area of the circle shown in the picture.

$\implies \pi (7)^{2}$

$\implies \huge\text{(}\dfrac{22}{7} \huge\text{)}(7)^{2}$ <em> </em>

$\implies \huge\text{(}\dfrac{22}{7} \huge\text{)}(7)(7)$

$\implies (22)(7)$

$\implies 154 \ \text{in}^{2}$

<h3>Solving Problem 5:</h3>

In this problem, we are given the diameter to be 24 kilometers. Since the radius of the circle is half the diameter, we can tell that the radius of the circle is 24/2 kilometers, which is 12 kilometers.

$\implies \pi (12)^{2}$

$\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (12)^{2}$

$\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (12)(12)$

$\implies \dfrac{3168}{7} \ \text{km}^{2}$

<h3>Solving Problem 6:</h3>

We are given the radius of circle, which is 3.5 in. Let us substitute the radius in the formula. Once substituted, we can simplify the expression obtained to determine the area of the circle shown in the picture.

$\implies \pi (3.5)^{2}$

$\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (3.5)^{2}$

$\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (3.5)(3.5)$

$\implies \huge\text{(}\dfrac{22}{2}\huge\text{)} (3.5) = (11) (3.5)$

$\implies 38.5 \ \text{m}^{2}$

Note: <em>The radius given in this problem was not clearly stated. If the radius I stated here, is incorrect, please notify me in the comments. Thanks!</em>

Learn more about area of circles: brainly.com/question/12414551

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2 years ago