1.

Show that (root3 +root 5)² is an irrational number.

Answer»

ANSWER:

Hence SHOWED

Step-by-step explanation:

To show (ROOT3 + root5)^2 is an irrational

Step 1 = Expand the NUMBER using (a + b)^2 = a^2 + 2(a)(b) + b^2

That is,

= (root3)^2 + 2(root3)(root5) + (root5)^2

= 3 + 2 root15 + 5

= 3 + 5 + 2 root15

= 8 + 2 root15

Step 2 = Follow the rules

As we know sum, difference, product and quotient of a rational(8) and irrational(2 root15) number is always irrational number.

HENCE SHOWED THAT (ROOT3 + ROOT5)^2 IS AN IRRATIONAL NUMBER


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