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Taya2010 [7]
3 years ago
10

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

Mathematics
2 answers:
natka813 [3]3 years ago
6 0

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.

sammy [17]3 years ago
5 0

<u>ANSWER:  </u>

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

<u>SOLUTION: </u>

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.

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