Question

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

Answer 1

Answer:

Option D. is correct.

Step-by-step explanation:

Let us assume that x = seven square root three plus two square root nine  

i.e. x = 7√3 + 2√9

⇒ x = 7√3 + 2 × 3 {Since 9 = 3²}

⇒ x = 7√3 + 6

Here, 7√3 is an irrational number and 6 is a rational number.

The answer is seven square root of three plus six is irrational because the sum of a rational number and an irrational number is an irrational number.

Therefore, option D. is correct.

Answer 2

Answer:

Option D

Step-by-step explanation:

Rational number is a number which can be expressed in the form $\frac{p}{q}$ where, p and q are integers. A rational number in decimal form as a terminating or repeating decimal.

An irrational number is a number that can't be expressed in the form $\frac{p}{q}$ and have a non-repeating, non-terminating decimal.

$7\sqrt{3}+2\sqrt{9}= 7\sqrt{3}+2\times3=7\sqrt{3}+6$

Square root of 9 is 3 as $3^{2}=3\times 3 =9$

Here, $7\sqrt{3}$ is an irrational number as $\sqrt{3}$ is an irrational number. The number 6 is a rational number.

So, the sum of a rational number and irrational number is always an irrational number.

Therefore, the correct option is option D