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3 years ago

Canh square roots be rational numbers ?

2 answers:

8 0

When the square root of a number is a whole number, this number is called a perfect square. ... Not all square roots are whole numbers. Many square roots are irrational numbers, meaning there is no rational number equivalent

irinina [24]3 years ago

7 0

Very good question, i’ll try to answer this as best as I can so here we go hope you enjoy

All rational numbers have the fraction form
,
a
b
,
where a and b are integers(≠0
b
≠
0
).

My question is: for what
a
and
b
does the fraction have rational square root? The simple answer would be when both are perfect squares, but if two perfect squares are multiplied by a common integer
n
, the result may not be two perfect squares. Like:
49→818
4
9
→
8
18

And intuitively, without factoring, =8
a
=
8
and =18
b
=
18
must qualify by some standard to have a rational square root.

Once this is solved, can this be extended to any degree of roots? Like for what
a
and
b
does the fraction have rational
n
th root?

Have a blessed day God bless.

You might be interested in

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given questions.

musickatia [10]

Answer:

a) Mean = $1,595.83

b) Median = $1,675

c) Mode = $1,950

d) Midrange = $1,475

- No, the resulting statistics are not representative of the population of all TVs that are 60 inches and larger because it is given that the dataset provided is for the selling prices of TVs that are 60 inches or larger and rated as a "best buy" by a popular magazine, hence, this dataset is representative of the best type of TVs that are 60 inches and larger and not all TV sets.

- The statistic that is most relevant other than the measures of central tendency is the standard deviation, a measure of dispersion It shows the variation of the selling prices of different best TVs that are 60 inches and larger, especially their variations from the mean.

Step-by-step explanation:

The data set for selling prices of TVs that are 60 inches or larger and rated as a "best buy" by a popular magazine.

1850 1950 1600 1950 1650 1000 1950 1400 1000 1700 1950 1150

a) Mean

The mean is the sum of all the variables in the distribution divided by the number of variables.

Mean = (Σx)/N = (1850+1950+1600+1950+1650+1000+1950+1400+1000+1700+1950+1150)/12

= (19,150/12) = $1,595.83

b) Median

The median is the variable that falls at the middle of the distribution when all the variables are arranged in ascending or descending order.

Arranging this dataset

1000, 1000, 1150, 1400, 1600, 1650, 1700, 1850, 1950, 1950, 1950, 1950

The numbers in the middle of this distribution include the sixth and seventh variables respectively, 1650 and 1700

Median = (1650+1700)/2 = $1,675

c) Mode

The mode is the variable with the highest frequency in the distribution. It is the variable that occurs the most in the distribution.

Evidently, the selling price with the highest frequency or the selling price that occurs the most in this distribution = $1950

d) Midrange

The midrange is given mathematically as

Midrange = [(Highest variable) + (lowest variable)] ÷ 2

Highest variable = 1950

Lowest variable = 1000

Midrange = (1950+1000)/2 = $1475

Hope this Helps!!!

4 0

3 years ago

James has noticed that the number of new tree branches that have grown on a tree in his backyard each year follows the sequence

eduard

Notice that the pattern is "previous term plus 2". This is an arithmetic sequence where the difference (d) equals +2

$a_{n}$ = a₁ + d(n - 1) ; where a₁ is the first term, d is the difference, and n is the term.

f(n) = 1 + 2(n - 1)

f(n) = 1 + 2n - 2

f(n) = 2n - 1

********************************

f(10) = 2(10) - 1

f(10) = 20 - 1

f(10) = 19

7 0

3 years ago

An isosceles triangle with angles b and c having the same measure is shown. Find the measure of each angle whose degree measure

Anton [14]

Answer:

A = 114°, B = C = 33°

Step-by-step explanation:

The triangle relationships let you write two equations:

A+B+C = 180

B=C

Substituting the expressions for A, B, and C, you have ...

(x+7y+41) +(2y+13) +(6x+15) = 180

7x +9y +69 = 180

7x +9y = 111

And the second equation gives ...

(2y+13) = (6x+15)

6x -2y =-2

3x -y = -1

Now, we can add 9 times this second equation to the first to eliminate the y-variable.

(7x +9y) +9(3x -y) = (111) +9(-1)

34x = 102

x = 3

Then the angle measures are ..

B = C = 6·3+15 = 33

A = 180 -2·33 = 114

The angles in the triangle are (A, B, C) = (114°, 33°, 33°).

8 0

4 years ago

...................................

miv72 [106K]

Answer:

it is A.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A bag contains x blue chips and y red chips. If the probability of selecting a red chip at random is 3/7, then x/y = ________.A.

LUCKY_DIMON [66]

Answer:

D. $\frac{4}{3}$

Step-by-step explanation:

We have been given that a bag contains x blue chips and y red chips. The probability of selecting a red chip at random is 3/7. We are asked to find the $\frac{x}{y}$ .

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$P(\text{Red})=\frac{\text{Number of red chips}}{\text{Total number of chips}}$

$P(\text{Red})=\frac{y}{x+y}$

Since we are told that probability of selecting a red chip at random is 3/7, so red balls are 3 and total balls are 7:

$P(\text{Red})=\frac{3}{x+3}$

Since total balls are 7, so we will get:

$x+3=7\\x=4$

Upon substituting $x=4\text{ and } y=3$ in expression $\frac{x}{y}$ , we will get:

$\frac{4}{3}$

Therefore, the value of $\frac{x}{y}$ is $\frac{4}{3}$ and option D is the correct choice.

7 0

3 years ago