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

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**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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