Slope between 1, 3/4 and 4, -3

Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$

horrorfan [7]

Answer:

$A +B+C+D = 3$ is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

$A+B+C+D = ?$ if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under $\sqrt$ (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

$\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}$

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, $A +B+C+D = 5+6-10+2 = \bold3$

5 0

3 years ago

1. Indicate whether the number is divisible by 2, by 3, or by 5.(Note: Some numbers may be divisible by more than one of these n

aleksklad [387]

1.

a.2,3,5 450/2=225 450/3=150 450/5=90

b.none

c.2 only 18,652/2=9,326

d.5 only 455/5=91

2.

a.3 and 5

b.3 and 7

c.19

d.7 and 21

3.

a.30

b.18

c.24

d.30

3 0

3 years ago

tenesa bought a 50 pound bag of flour for her bakery. she used 13.65 pounds of flour. how many pounds of flour are left in the b

saw5 [17]

Answer: 36.35

work:
50 - 13.65 = 36.35

4 0

3 years ago

Read 2 more answers

Points A B C D and E are collinear and in that order. Find AC if AE=x+50 and CE=x+32

Lana71 [14]

Answer:

18

Step-by-step explanation:

Points A B C D and E are collinear.

$\therefore AE = AC + CE\\\therefore AC = AE - CE\\\therefore AC = x + 50 - (x + 32) \\\therefore AC = x + 50 - x - 32 \\\therefore AC = 50 - 32 \\ \huge \red{ \boxed{\therefore AC = 18}}$