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3 years ago

Classify the following numbers as rational or irrational. √23

Mathematics

2 answers:

m_a_m_a [10]3 years ago

7 0

Answer:

√23 is an Irrational Number

Step-by-step explanation:

√23 = 4.79 is not a pefect square so its an irrational number

harina [27]3 years ago

5 0

Answer:

Irrational

Step-by-step explanation:

Unless a radical solves out to be a whole number, rads are irrational.

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Conjugate/Rational Number?

hram777 [196]

Answer:

1) $\dfrac{2}{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}$

2) $-\dfrac{5}{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}$

3) $\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } =\dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}$

4) $\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \sqrt{3} + \dfrac{\sqrt{6} }{3}$

5) $\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }= \dfrac{\sqrt{15} - \sqrt{6} }{3}$

Step-by-step explanation:

The rationalization of the denominator of the surds are found as follows;

1) $\dfrac{2}{\sqrt{5} }$

$\dfrac{2}{\sqrt{5} } \times \dfrac{\sqrt{5} }{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}$

$\dfrac{2}{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}$

2) $-\dfrac{5}{\sqrt{3} }$

$-\dfrac{5}{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}$

$-\dfrac{5}{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}$

3) $\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} }$

$\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } \times \dfrac{ \sqrt{10} }{\sqrt{10} } = \dfrac{\sqrt{20} + \sqrt{50} }{10 } = \dfrac{2\cdot \sqrt{5} + 5 \cdot \sqrt{2} }{10} = \dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}$

$\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } =\dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}$

4) $\dfrac{3 + \sqrt{2} }{\sqrt{3} }$

$\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \dfrac{3 \cdot \sqrt{3}+\sqrt{6} }{3 } = \sqrt{3} + \dfrac{\sqrt{6} }{3}$

$\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \sqrt{3} + \dfrac{\sqrt{6} }{3}$

5) $\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }$

$\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} } = \dfrac{\sqrt{5} - \sqrt{2} }{\sqrt{5} - \sqrt{2} } = \dfrac{\sqrt{15} -\sqrt{6} }{5 - 2} = \dfrac{\sqrt{15} - \sqrt{6} }{3}$

$\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }= \dfrac{\sqrt{15} - \sqrt{6} }{3}$

6) $\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} }$

$\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} } \times \dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} = \dfrac{\sqrt{21} + \sqrt{35}}{{3} + {5}} = \dfrac{\sqrt{21} + \sqrt{35}}{8}$

$\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} } \times \dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} =\dfrac{\sqrt{21} + \sqrt{35}}{8}$

8 0

3 years ago

Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two num

eduard

Answer:

The value of two numbers is x=49 and y=26 and the corresponding equation for the given condition is x +y =75

<u>Explanation:</u>

Given:

Sum of two numbers is 75

One number is 23 more than other

To find:

Frame the equation for the above condition and find the value of two numbers.

Solution:

From the given we know that the sum of two numbers is 75

Let x and y be the numbers, such that the equation is framed as

x +y =75

And we also know that one number is 23 more than other, so we can say either x or y has a greater one

Here I say x is 23 more than y such that,

x=23+y

Substitute the value of x in the equation and we know

x + y=75 and x=23+y we get,

23+y+y=75

23+2y=75

2y=75-23

2y=52

y=26

Since x=23+y as already stated we get as

x=23+26=49

Result:

Thus the equation for the above given conditions is x +y =75 and the values of two number is 49 and 26

8 0

3 years ago

The difference of the squares of two positive consecutive even integers is 28. find the integers.

Klio2033 [76]

The integers are 8 and 6:

${8}^{2} - {6}^{2} = 64 -36 = 28$

7 0

3 years ago

If (-3, y) lies on the graph of y = (1/2)^x, then y =

labwork [276]

$\text{If (-3, y) lies on the graph of}\ \ y = \left(\dfrac{1}{2}\right)^x, \text{then substitute x = -3}\\\text{ to the equation and calculate y}:\\\\y=\left(\dfrac{1}{2}\right)^{-3}=(2)^3=8\\\\Answer:\ \boxed{y=8}\\\\Used:\ a^{-n}=\dfrac{1}{a^n}$

6 0

3 years ago

A board is 4 feet 8 inches long how long is the board inches

Otrada [13]

the board is 56 inches long.

how i did this was

12 * 4 = 48

48 + 8 = 56

<em>hope this helps :)</em>

7 0

3 years ago

Classify the following numbers as rational or irrational. √23​

Classify the following numbers as rational or irrational. √23