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
azamat
3 years ago
6

Square root of -30 over square root of -10

Mathematics
1 answer:
Nuetrik [128]3 years ago
5 0

Answer:  The answer is:  " √3 " .

_______________________________________

           →   The simplified expression is:  " √3 " .

_______________________________________

Step-by-step explanation:

_______________________________________

We are given:

_______________________________________

  →    \frac{\sqrt{-30}}{\sqrt{-10}}  ;

_______________________________________

Note the "imaginary number" —  " √(-1) " —

               which is represented by the symbol:  " *i* "  .

_______________________________________

So, let us factor out Both the <u>numerator</u> And the <u>denominator</u>:

_______________________________________

Start with the "numerator" ; as follows:

The numerator is:  √(-30) ;  which factors into:

                       

                              →   √-1 * √30 ;

_____________________________________

Note that:  " √-1 " ; is an <u>imaginary number</u>; which is represented

                              by the symbol:  " *i* "  .

As such, we can rewrite the <u>numerator</u> as:

                             →   *i* √30  .

______________________________________

The denominator is:  √(-10) ; which factors into:

                              →  √-1  * √10  ;

______________________________________

As noted above:

           →    " √-1 "  ;   is an <u>imaginary number</u>; which is represented

                                    by the symbol:  " *i* "  .

As such, we can rewrite the denominator as:

                             →   *i* √10   .

______________________________________

Now, let us rewrite the entire expression:

______________________________________

          ( *i* √30)

       ____________

          ( *i* √10)    

______________________________________

<u>Note</u>:  The  *i*  symbols "cancel out" to:  " 1 " ;  

 

   →   { since:  any "non-zero value" ;  divided by "that same value" ;

                    is equal to:  "1 " .} ;

   →   { i.e.,  in our case:  [ *i*  ÷  *i* ] ;  that is;  " [*i* / *i* ], equals : " 1 " .}.

______________________________________

And we are left with:

______________________________________

   →  " \frac{\sqrt{30}}{\sqrt{10}} " .

______________________________________

Note that both the numerator and the denominator are "square roots" —    

           and furthermore — are square roots of a "positive number".

Specifically, the "numerator" is:  " √30 " ;

        And  the "denominator is:  " √10 " .

______________________________________

  →    Note that the numerator:  " √30 " ;

                →    can be factored into:  "√10 * √3 " ;

  →    And that the "denominator" ;  which is:  " √10 " ;  is one of the aforementioned 'factors' of the "numerator" .

_____________________________________

Let us rewrite the expression — and further simplify:

          →    \frac{\sqrt{30}}{\sqrt{10}}   ;

_____________________________________

   =   \frac{(\sqrt{10} *\sqrt{3})}{\sqrt{10}}  ;

_____________________________________

<u>Note</u>:  The "(√10)" values,  "cancel out"  to:  "1" ;

       

→  {since:  any "non-zero value" ;  divided by "that same value" ;

                    is equal to:  "1 " .} ;

                                         

         →   { i.e.,  in our case:  [" √10 ÷ √10 " ] ;  

         →   that is;  [ " \frac{\sqrt{10}}{\sqrt{10}} " ]" ;

                                       →   equals : " 1 " .}.

_____________________________________

→   and we are left with:  " (√3) / 1 " ;

           →  which equals:   " √3  "  ;  

           →  which is our answer.

_____________________________________

Hope this is helpful to you.

     Best wishes in your academic endeavors

             — and within the "Brainly" community!

_____________________________________

You might be interested in
The regular price of a dvd is $24?. During a sale, the price of a dvd is marked down 30%. What will the sale price of the dvd?
Tatiana [17]

If a $24 dvd is marked down by 30% then the cost of the dvd would be 70% of the original cost. 100% - 30% = 70%

70% of 24 can be expressed as 0.7 x 24.

The answer is $16.80.

Hope this helps :)

4 0
3 years ago
PLEASE ANSWERRRRRR
viva [34]

Answer:

A. y=-2x+5

Step-by-step explanation:

y=mx+b , m represents slope (-2), b represents y intercept (5)

8 0
3 years ago
Read 2 more answers
What is the answer to the question
Minchanka [31]
D'
you can't use the same single letter to mark a new point.
3 0
3 years ago
Enter the coordinates of the point on the unit circle at the given angle. 135° (-VII, VI Enter​
vekshin1
Related angle is 45 degrees, set up a triangle and use exact trig values to solve for x and y, then rationalise the denominators

4 0
3 years ago
The probability that a certain machine will produce a defective item is 0.20. if a random sample of 20 items is taken from the o
GenaCL600 [577]
Use binomial distribution, with p=0.20, n=20, x=3
P(X=x)=C(n,x)p^x (1-p)^(n-x)

P(X>=3)
=1-(P(X=0)+P(X=1)+P(X=2))
=1-(C(20,0)0.2^0 (0.8)^(20-0)+C(20,1)0.2^1 (0.8)^(20-1)+C(20,2)0.2^2 (0.8)^(20-2))
=1-(0.0115292+0.057646+0.136909)
=1-0.206085
=0.793915
7 0
3 years ago
Other questions:
  • trip in space 4.5 x 10 exponent 9 miles will take 9 1/2 years how many miles will space craft travel per year
    8·1 answer
  • Plz subscribe to my channel Mr.PorkXchop 101
    15·2 answers
  • Mr. Sanchez earns 4% commission on each car he sells. How much commission does he earn on a $15,000 car?
    8·2 answers
  • How can you use models to estimate percent questions?
    11·1 answer
  • Li Na is going to plant 63tomato plants and 81 rhubarb plants.
    5·1 answer
  • Tonya’s grandma has two pieces of cloth. She wants to estimate how much longer one piece is than the other. She will estimate to
    10·2 answers
  • Scores on a standardized test are normally distributed find percentage
    14·1 answer
  • 100% - 9/10<br> Pleeaaase help
    7·2 answers
  • Ben bought the enormous box of juice shown below. He drinks 450 cubic centimeters of juice each day. How many days does it take
    10·2 answers
  • I need help with this geometry proof
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!