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Ulleksa [173]
3 years ago
5

Prove that root 7 is irrational by the method of contradiction

Mathematics
1 answer:
Alchen [17]3 years ago
8 0

Let assume that \sqrt7 is a rational number. Therefore it can be expressed as a fraction \dfrac{a}{b} wherea,b\in\mathbb{Z} and \text{gcd}(a,b)=1.

\sqrt7=\dfrac{a}{b}\\\\7=\dfrac{a^2}{b^2}\\\\a^2=7b^2

This means that a^2 is divisible by 7, and therefore also a is divisible by 7.

So, a=7k where k\in\mathbb{Z}

(7k)^2=7b^2\\\\49k^2=7b^2\\\\7k^2=b^2

Analogically to a^2=7b^2 ------- b^2 is divisible by 7 and therefore so is b.

But if both numbers a and b are divisible by 7, then \text{gcd}(a,b)=7 which contradicts our earlier assumption that \text{gcd}(a,b)=1.

Therefore \sqrt7 is an irrational number.

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1000 times 32.18 what’s the answer plzz help me
Dvinal [7]
When multiplying by a power of 10 (10, 100, 1000, etc.) we can just move the decimal of the other number to the right. Since were multiplying by 1000, we move the decimal to the right 3 times. The answer is 32,180.
4 0
3 years ago
5. Simplify the expression,<br> (-2 - 5i) - (-4+6i)<br> 2 - 11i<br> -2+i<br> -6 + 11i<br> -5i
monitta

\qquad\qquad\huge\underline{{\sf Answer}}♨

Let's simplify ~

\qquad \sf  \dashrightarrow \:( - 2 - 5i) - ( - 4 + 6i)

\qquad \sf  \dashrightarrow \: - 2 - 5i +  4  -  6i)

\qquad \sf  \dashrightarrow \: - 2 +  4   - 5i-  6i)

\qquad \sf  \dashrightarrow \:2 - 11i

Therefore, A is the Correct choice !

7 0
2 years ago
(1) 2y×5x(7÷18)-1+3?<br><br><br>And <br><br>(2) 45÷28(3x+6y)=
Alenkinab [10]

Answer:

not really sure for number one

1. 1.56y × 3.9x

2. 4.8x + 9.6y

6 0
3 years ago
3+×/2=10 <br> Is ×/2=7<br> And does ×=14
adoni [48]

3+\dfrac{x}{2}=10\qquad|\text{subtract 3 from both sides}\\\\\dfrac{x}{2}=7\qquad|\text{multiply both sides by 2}\\\\\boxed{x=14}

7 0
3 years ago
a point on a perpendicular bisector is 7cm from each endpoint of the bisected segment and 5cm from the point of intersection. Wh
love history [14]

9514 1404 393

Answer:

  about 9.80 cm

Step-by-step explanation:

The length of half the segment (h) can be found from the Pythagorean theorem:

  h² +5² = 7²

  h² = 7² -5² = 49 -25 = 24

  h = √24 = 2√6

This is half the segment length, so the whole segment length is ...

  L = 2h = 2(2√6)

  L = 4√6 ≈ 9.7980

The length of the segment is 4√6 ≈ 9.80 cm.

8 0
3 years ago
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