5-3√5 prove that it is a rational or irrational number

1.	5-3√5 prove that it is a rational or irrational number
Answer» Answer: 5-3 $\sqrt{5}$ is rational or IRRATIONAL number. Step-by-step EXPLANATION: LETS assume that 5-3 $\sqrt{5}$ is rational number. where as p and Q are co- primes. 5-3 $\sqrt{5}$ =p/q squaring on both sides. (5-3 $\sqrt{5}$ )2=(p/q)2 (5)2+2(5)(-3 $\sqrt{5}$ )+(2)2=p2/q2 25-30 $\sqrt{5}$ +4=p2/q2 -5 $\sqrt{5}$ +4=p2/q2 -5 $\sqrt{5}$ =p2/q2-4 $\sqrt{5}$ =p2/q2-4/5. THEREFORE our assumstion is wrong. p ,q,4,5 are integers Therefore 5-3 $\sqrt{5}$ is irrational.

Answer»

Answer:

5-3 $\sqrt{5}$ is rational or IRRATIONAL number.

Step-by-step EXPLANATION:

LETS assume that 5-3 $\sqrt{5}$ is rational number.

where as p and Q are co- primes.

5-3 $\sqrt{5}$ =p/q

squaring on both sides.

(5-3 $\sqrt{5}$ )2=(p/q)2

(5)2+2(5)(-3 $\sqrt{5}$ )+(2)2=p2/q2

25-30 $\sqrt{5}$ +4=p2/q2

-5 $\sqrt{5}$ +4=p2/q2

-5 $\sqrt{5}$ =p2/q2-4

$\sqrt{5}$ =p2/q2-4/5.

THEREFORE our assumstion is wrong.

p ,q,4,5 are integers

Therefore 5-3 $\sqrt{5}$ is irrational.

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5-3√5 prove that it is a rational or irrational number​

5-3 is rational or IRRATIONAL number.

LETS assume that 5-3 is rational number.

where as p and Q are co- primes.

5-3=p/q

squaring on both sides.

(5-3)*2=(p/q)*2

(5)*2+2(5)(-3)+(2)*2=p*2/q*2

25-30+4=p*2/q*2

-5+4=p*2/q*2

-5=p*2/q*2-4

=p*2/q*2-4/5.

THEREFORE our assumstion is wrong.

p ,q,4,5 are integers

Therefore 5-3 is irrational.

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5-3√5 prove that it is a rational or irrational number

5-3 $\sqrt{5}$ is rational or IRRATIONAL number.

LETS assume that 5-3 $\sqrt{5}$ is rational number.

5-3 $\sqrt{5}$ =p/q

(5-3 $\sqrt{5}$ )2=(p/q)2

(5)2+2(5)(-3 $\sqrt{5}$ )+(2)2=p2/q2

25-30 $\sqrt{5}$ +4=p2/q2

-5 $\sqrt{5}$ +4=p2/q2

-5 $\sqrt{5}$ =p2/q2-4

$\sqrt{5}$ =p2/q2-4/5.

Therefore 5-3 $\sqrt{5}$ is irrational.