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KonstantinChe [14]
4 years ago
10

Prove that 7 + 3 root 2 is not a rational number​

Mathematics
2 answers:
Tanya [424]4 years ago
5 0

Answer:

Step-by-step explanation:

let 7 + 3√2 be an rational number where

7+3√2 = a/b [ a and b are coprime and b is not equal to zero]

3√2= a/b-7

3√2 =( a-7b) /b

√2 = (a-7b) /3b .....(i)

Now ,from equation (i) ,we get that √2 is rational but we know that √2 is irrational. so actually 7 + 3√2 is irrational not rational. thus our assumption is wrong. The number is irrational.

In-s [12.5K]4 years ago
4 0

Answer:

Prove by contradiction.

See below.

Step-by-step explanation:

Assume it is rational, then:

Let x = 7 + 3√2 = p/q      where p and q are integers and p/q is in simplest form.

x^2 = 49 + 42√2  + 18 = p^2/q^2

67q^2 = p^2  - 42√2q^2

67q^2 - p^2 = -42√2 q^2

67q^2 - p^2 is rational and q^2 is rational so that makes -42√2  rational.

but we know that -42√2  is irrational, so our original assumption is not true.

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avanturin [10]

Answer:

6  socks

Step-by-step explanation:

What we must do is calculate the probability of this happening, that he takes out two black socks in the first two taken out.

There are 12 black socks and in total they are 24, therefore the probability of drawing 1 is:

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the final probability is the multiplication of these events:

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P = 0.24

Now, to know how many you should get, we multiply the probability by the total number of socks, that is:

0.24 * 24 = 5.76

So you must take out at least 6 socks for the above to happen.

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3 years ago
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Answer:

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Based on the graph below, which point is a solution?
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3 years ago
Question: A canary's beak is, at most, 20mm long. Which algebraic inequality represents this situation?
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Answer:

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Step-by-step explanation:

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Word "at most" means "the maximum".

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or

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