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Troyanec [42]
3 years ago
10

What is a counterexample of the statement “all square roots are irrational”

Mathematics
1 answer:
skad [1K]3 years ago
3 0

Rather than trying to guess and check, we can actually construct a counterexample to the statement.

So, what is an irrational number? The prefix "ir" means not, so we can say that an irrational number is something that's not a rational number, right? Since we know a rational number is a ratio between two integers, we can conclude an irrational number is a number that's not a ratio of two integers. So, an easy way to show that not all square roots are irrational would be to square a rational number then take the square root of it. Let's use three halves for our example:

\sqrt{(\frac{3}{2})^2}=\\\sqrt{\frac{9}{4}}=\\\frac{3}{2}

So clearly 9/4 is a counterexample to the statement. We can also say something stronger: All squared rational numbers are not irrational number when rooted. How would we prove this? Well, let \frac{a}{b} be a rational number. That would mean, \frac{a^2}{b^2}, would be a/b squared. Taking the square root of it yields:

\sqrt{\frac{a^2}{b^2}}}=\\ \frac{\sqrt{a^2}}{\sqrt{b^2}}=\\ \frac{a}{b}

So our stronger statement is proven, and we know that the original claim is decisively false.

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if the length of the rectangle is twice the width and the perimeter of the rectangle is 30 centimeters what is the length of the
Dominik [7]
If the perimeter equals 30 and the length is twice the width, then the length is equal to 20 and the width is equal to 10.

7 0
3 years ago
Jodi has two bank accounts. Her parents started Account A for her. It currently has $100 in it, and Jodi deposits $20 into it ea
Law Incorporation [45]

Answer:

(f+g)(x) = 60x + 400

Step-by-step explanation:

Given :

Amount in account A:

f(x) = 20x + 100

Amount in account B :

g(x) = 40x + 300

Total amount in Account A and B:

f(x) + g(x) = (20x + 100) + (40x + 300)

(f+g)(x) = (20x + 40x) + (100 + 300)

(f+g)(x) = 60x + 400

6 0
3 years ago
Find the value of x, o is the centroid
Ray Of Light [21]

Answer:

x = 14

Step-by-step explanation:

In the triangle O is the centroid.  

Now, we know that the centroid divides the medians in the 2 : 1 ratio that means the distance from the centroid to the vertex and the distance from the centroid to the opposite side remains in 2 : 1 ratio.

So, from the given diagram we can write  

\frac{3x}{2x - 7} = \frac{2}{1}

⇒ 3x = 4x - 14

⇒ x = 14 (Answer)

3 0
3 years ago
A tourist first walked 17km with a speed of v km/h. Then he hiked 12 km uphill with the speed that was 2 km/hour less than his o
ExtremeBDS [4]

Answer: t=\frac{17}{v}+\frac{12}{v-2}


Step-by-step explanation:

Given: A tourist first walked 17km with a speed of v km/h.

Since Speed=\frac{distance}{time}

therefore, Time=\frac{distance}{speed}

Let t_1 be the time he walked with speed v.

then t_1=\frac{17}{v}

Also he hiked 12 km uphill with the speed that was 2 km/hour less than his original speed.

Let t_2 be the time he hiked 12 km,

Then t_2=\frac{12}{v-2}

The total time for the whole trip is given by:-

t=t_1+t_2=

Substitute the values of t_1 and t_2 in the equation, we get

t=\frac{17}{v}+\frac{12}{v-2}

4 0
3 years ago
Zachary purchased a computer for 1800 on a payment plan. Three months after he purchased the computer, his balance was 1350. Fiv
zubka84 [21]

<u>Solution-</u>

Zachary purchased a computer for 1800 on a payment plan.  (Initial Money)

3 months after he bought the computer, his balance was 1350. (Money after 3 months)

Total money paid in 3 months = 1800-1350 = 450

Money paid per month = 450/3 = 150

5 months after he bought the computer, his balance was 1050.

Total spent = 1800-1050 = 750 = (5× 150)

So the equation that models the balance b after m months,

b = 1800 - m(150)

∴ Here, the slope signifies the constant monthly deduction of $150.


3 0
3 years ago
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