Question

show that 7root3-3 is also an irrational number​

Answer 1

7√3 - 3

_________ [ GIVEN ]

• We have to prove it Irrational number.

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Let us assume that 7√3 - 3 is rational number.

→ 7√3 - 3 = a/b

Here, a and b are co-prime numbers

→ 7√3 = (a/b) + 3

→ 7√3 = (a + 3b)/b

→ √3 = (a + 3b)/7b

Here, (a + 3b)/7b is rational number.

So, √3 is also a rational number.

But we know that √3 is irrational number.

So, our assumption is wrong.

7√3 - 3 is irrational number.

_______ [ PROVED ]

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