Question

prove that 10 + 5√3 is an irrational number
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Do answer this fast !!​

Answer 1

Answer:

10+5√3

Let 10+5√3 is a rational number

So, it is equal to a /b

10+5√3= a/b

5√3 =a/b-10

by taking LCM

5√3=a-10b/b

√3= a-10b/5b

√3 is a irrational number. So, 10+5√3is a also a irrational number.

HOPE IT IS HELPFUL...

Answer 2

Answer:

cuemath_logo

Show that 5 - √3 is irrational

Solution:

We will use the contradiction method to show that 5 - √3 is an irrational number.

Let us assume that 5 - √3 is a rational number in the form of p/ q where p and q are coprimes and q ≠ 0.

5 - √3 = p /q

Add √3 to both sides.

5 - √3 + √3 = p /q + √3

5 = p/ q + √3

Subtract both sides p/ q.

5 - p/ q = √3

(5q - p)/ q = √3

Since we already know that √3 is an irrational number.

Thus, a rational number can not be equal to an irrational number

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