Question

Prove that 15 is irrational.​

Answer 1

Step-by-step explanation:

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Let us assume that √15 is a rational number

Where a, b belongs to integers and q ≠ 0

√15 = $\frac{a}{b}$

Now,

Squaring on both sides

• (√15) ² = ( $\frac{a}{b}$ ) ²

• 15 = $\frac{a²}{b²}$

• 15b² = a²

15 is divisible by a²

b also divisible by a

Let, a = 15c

Now apply "a" value in above equation

• a² = 15b²
• (15c) ² = 15b²
• 225c² = 15b²
• 15c² = b²

15 is divisible by b²

15 is also divisible by b

:. 15 is divisible by both a and b

Which is not a co-prime .

Hence, Our assumption is wrong

√15 is a irrational number

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