Question

Solve seven square root three plus two square root nine and explain whether the answer is rational or irrational.

Answer 1

ANSWER:  

Seven square root three plus two square root nine is irrational and the value is 18.12

SOLUTION:

Given, seven square root three plus two square root nine

= seven square root three + two square root nine

$\begin{array}{l}{=7 \sqrt[2]{3}+2 \sqrt[2]{9}} \\ {=7 \sqrt[2]{3}+2 \sqrt[2]{3^{2}}} \\ {=7 \sqrt[2]{3}+2 \times 3} \\ {=7 \sqrt[2]{3}+6}\end{array}$

We know that, $\sqrt[2]{3}$  is irrational as it cannot be expressed as ratio of two integers.

Now, $7 \sqrt[2]{3}+6$ is also irrational, because sum of rational and irrational is always irrational.

$\begin{array}{l}{\text { On solving } 7 \sqrt[2]{3}+6,} \\ {7 \sqrt[2]{3}+6=7(1.732)+6=18.12}\end{array}$

Hence, seven square root three plus two square root nine is irrational.

Answer 2

Answer:

The answer to the given question is irrational.

Step-by-step explanation:

A rational number can be expressed as a fraction, while irrational number is a real number that cannot be expressed as a simple fraction.

From the question,

 $7\sqrt{3} + 2\sqrt{9}$  = $7\sqrt{3} + 2\sqrt{3^{2} }$

                    = $7\sqrt{3} + 2(3)^{\frac{2}{2} }$

                    = $7\sqrt{3} + 6$

But, $7\sqrt{3} + 6$ would give an irrational answer.

Thus, seven square root three plus two square root nine equals 18.12435565 which is irrational.