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DENIUS [597]
3 years ago
7

Simplify radicals problems attached please help!

Mathematics
1 answer:
Finger [1]3 years ago
8 0

Answer:

  G7.  (2√3)/3

  G8.  -2+√7

  G9.  (6 +2√2 -3√3 -√6)/7

Step-by-step explanation:

G7.

\dfrac{2}{\sqrt{3}}=\dfrac{2}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}

__

G8.

\dfrac{3}{2 +\sqrt{7}}=\dfrac{3}{2+\sqrt{7}}\cdot\dfrac{2-\sqrt{7}}{2-\sqrt{7}}=\dfrac{6-3\sqrt{7}}{2^2-(\sqrt{7})^2}\\\\=\dfrac{6-3\sqrt{7}}{-3}=\sqrt{7}-2

__

G9.

\dfrac{2-\sqrt{3}}{3-\sqrt{2}}=\dfrac{2-\sqrt{3}}{3-\sqrt{2}}\cdot\dfrac{3+\sqrt{2}}{3+\sqrt{2}}=\dfrac{(2-\sqrt{3})(3+\sqrt{2})}{9-2}\\\\=\dfrac{6+2\sqrt{2}-3\sqrt{3}-\sqrt{6}}{7}

_____

<em>Comment on the problems</em>

In most cases, these expressions are the simplest possible (take the least amount of ink to draw, and take the fewest math operations to evaluate). What seems to be intended is that the denominator be made a rational number. This is done by multiplying the given fraction by a fraction equal to 1 that has the same denominator but with the sign of the radical reversed (unless, as in the first case, the radical is by itself).

The purpose of doing this is to take advantage of the fact that (a-b)(a+b) = a²-b², so if "a" or "b" is a square root, that root will not be seen in the product. In problem G9, we see this can make the numerator quite messy--not exactly a simpler form--but all the irrational numbers are in the numerator.

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Which of the following is true about the expression V3*2
likoan [24]

Answer:

B

Step-by-step explanation:

√3 is an irrational number, 2 is a rational number.

the product of this will be 2√3 in surds form, and when pressed into the calculator will provide you with an irrational answer.

7 0
2 years ago
on Saturday Leo and his brother drove into town to visit their mom Leo is trying to remember how much he spent on gas and tolls
Gwar [14]

Let t be the number of tolls they crossed.

Amount they spent at each toll = $1.75.

Amount they spent at gas station = $28.

Let C be the total amount they spent on gas and tolls.

If they crossed 1 toll, then

C = 28 + 1.75(1).

If they crossed 3 tolls, then,

C = 28 + 1.75(3)

If they crossed t tolls, then,

C = 28 + 1.75t

Here, the terms are 28 and 1.75t and the factors are 1.75 and t.

8 0
3 years ago
Find the equation of the line shown
Finger [1]

Answer:

y=x+1

Step-by-step explanation:

As you can see, the slope is clearly 1 and the line starts at (0, 1), which is its y-intercept.

Plug the variables into this formula: y=mx+b, then you will get y=x+1.

3 0
3 years ago
I HONESTLY NEED HELP!!
Natali5045456 [20]

Answer:

B

Step-by-step explanation:

an additional hour of walking is associated with an additional 0.7 mile walk

7 0
3 years ago
A line segment has endpoints (-5, 10) and (a,b) . If the midpoint of the segment is (13, -2), what is the absolute difference be
AlexFokin [52]
If the line segment point is D(-5, 10) and E(a,b) and the  midpoint of the segment is F(13, -2) that mean 
DE= 2*DF

You can directly find the distance of AC 
Xdf= Xf-Xd= 13 - (-5)= 18
Ydf= Yf - Yd= -2 - 10= -12

Then add the distance of AB( which is 2*AC) to point D
Xe= a = Xd + 2*Xdf 
a= -5 +2*18= 31

Ye= b = Yd + 2Yf
b= 10+ 2*-12= -14

<span>absolute difference between a and b:
|b-a|= </span>|-14-31|= 45
7 0
2 years ago
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