1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
guapka [62]
2 years ago
13

Rationalise the denominator of (12)/(\sqrt(10)+\sqrt(7)+\sqrt(3))

Mathematics
1 answer:
jasenka [17]2 years ago
5 0

Answer:

\frac{12}{\sqrt{10} +\sqrt{7} +\sqrt{3} }=\frac{6\sqrt{147} +6\sqrt{63}-6\sqrt{210}  }{21 }

Step-by-step explanation:

\frac{12}{\sqrt{10} +\sqrt{7} +\sqrt{3} }

=\frac{12\left( \sqrt{10} -\left( \sqrt{7} +\sqrt{3} \right)  \right)  }{(\sqrt{10}+(\sqrt{7} +\sqrt{3 } ))( \sqrt{10} -( \sqrt{7} +\sqrt{3}))}

=\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right)  }{\sqrt{10^2} -(\sqrt{7} +\sqrt{3})^2}

\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right)  }{10-(10+2\sqrt{21} )} }

=\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right)  }{-2\sqrt{21} }

=\frac{-6\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right)  }{\sqrt{21} }

=\frac{-6\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right)  }{\sqrt{21} } \times\frac{\sqrt{21} }{\sqrt{21} }

=\frac{-6\sqrt{21} \left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right)  }{21 }

=\frac{-6\sqrt{210} +6\sqrt{147} +6\sqrt{63}  }{21 }

=\frac{6\sqrt{147} +6\sqrt{63}-6\sqrt{210}  }{21 }

<u><em>Remark</em></u>:

You can simplify moreover if you want to.

You might be interested in
What is an equation of the line that passes through the points (3,-3) and (-3,-3)?
victus00 [196]
First find the gradient of the line
Change in y/change in x
-3–3/-3-3
0/-6
=0 ( so the gradient m is equal to zero)

Y=0x+c

Input the coordinates of one point to find c

-3=(0*3)+c
-3=c


So the equation is
Y= -3


3 0
3 years ago
Write down a fraction whose value lies between 3 and 4; whose denominator is a multiple of 5; whose numerator is a multiple of 1
slamgirl [31]

Answer:

  33/10 and 55/15

Step-by-step explanation:

Possible denominators that are multiples of 5 less than 17 are 5, 10, 15.

Corresponding numerator ranges are [15, 20], [30, 40], and [45, 60]. In only two of these ranges are there any multiples of 11.

  33 in [30, 40]

  55 in [45, 60]

So, there are only two possible fractions meeting your requirement:

  33/10 and 55/15

6 0
3 years ago
The function f(x)=x^2 is graphed on the coordinate grid.
Aleksandr [31]
<h3>Answer:</h3>
  • graphed below.
<h3>Explanation:</h3>
  • vertex: (0, 0)

other points:

<u>x    y</u>

-2  12

-1   3

0   0

1    3

2   12

7 0
2 years ago
Read 2 more answers
PLEASE HELP ASAP!! WILL MARK BRAINLIEST!!
Hitman42 [59]
A. This is a function
4 0
3 years ago
Read 2 more answers
What is 7a +6c+9a-15c
jeka94

                               7a + 6c + 9a - 15c

-- Look for all the 'a's      7a,  9a

-- Addum up                    16a

-- Look for all the 'c's      6c,  -15c

-- Addum up                     -9c

-- Write the results         16a - 9c
3 0
3 years ago
Read 2 more answers
Other questions:
  • A market researcher obtains a list of all streets in a town. She randomly samples 10 street names from the list, and then admini
    10·1 answer
  • In science class; abigail's frog weighed 0.88 kilogram. what is the value of the digit in the tenths
    6·1 answer
  • The average cost of a compact car at a certain dealership over the last 10 years has ranged from $14,000 to $18,500. Suppose you
    10·1 answer
  • What is the answer to <br> –3x2+7=-2x
    13·1 answer
  • What is -7 divided by 1/2?
    10·2 answers
  • Solve the equation if there is no solution, write no solution | m | / 2 - 1 = -3
    9·2 answers
  • A special roulette wheel, which has an equal number of red and black spots, has come up red four times in a row. Assuming that t
    6·1 answer
  • What is the solution to the following equation ? plz help x +(-21)=8
    13·1 answer
  • An office needs 300 envelopes. If there are 30 envelopes in each box, how many boxes should the office buy?
    13·2 answers
  • 1. A small garden has a perimeter of 24 1/4 ft. If the lengths is 8 ft, what is the area of the garden.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!