Question

Examine whether numbers(3-root3) (3+root 3) is rational or irrational

Answer 1

Step-by-step explanation:

(3-√3)(3+√3)

(a-b)(a+b)

by the formula we got

ans=6

it is rational no.

Answer 2

Question: Examine whether number $(3-\sqrt{3} )(3+\sqrt{3} )$ is rational or irrational.

Answer:

The number $(3-\sqrt{3} )(3+\sqrt{3} )$ is rational.

Step-by-step explanation:

Rational number: The number which can be written in the p/q form, q≠0, where p and q are integers.

Irrational number: The number which cannot be written in the p/q form, q≠0, where p and q are integers.

Recall the identity,

$(a+b)(a-b)=a^2-b^2$

Step 1 of 1

To check: The number $(3-\sqrt{3} )(3+\sqrt{3} )$ is rational or irrational.

Consider the given number as follows:

$(3-\sqrt{3} )(3+\sqrt{3} )$ . . . . . (1)

Here, $a=3$ and $b=\sqrt{3}$

Notice that the number $3$ is a rational number and the number $\sqrt{3}$ is an irrational number.

Simplify the expression (1) using the identity as follows:

⇒ $3^2-(\sqrt{3} )^2$

⇒ $9-3$

⇒ $6$

⇒ $(3-\sqrt{3} )(3+\sqrt{3} )=6$

Clearly, the number $6$ is a rational number and can be written in the p/q form as $\frac{6}{1}$.

Therefore, the number $(3-\sqrt{3} )(3+\sqrt{3} )$ is a rational number.

#SPJ2