Question

the number to minus root 2 x 2 + root 2 is a rational number or irrational number​

Answer 1

Answer:

22–√=2.82...22=2.82... is irrational. A proof is as so:

Let xx be an irrational number and p=mnp=mn for integers m,nm,n. pp is rational.

We want to show that pxpx is irrational. We shall do this by contradiction, as follows:

Assume px=mxnpx=mxn is rational, and equal to q=abq=ab. We then have that mxn=ab⟹x=anbmmxn=ab⟹x=anbm, which is false, and thus we prove that pxpx is irrational.

Since there are no restrictions on pp or xx, we have shown that a rational number times an irrational number is irrational, therefore 22–√22 is irrational

Step-by-step explanation:

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