Question

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

A.The answer nine square root of twelve is rational because the sum of a rational number and irrational number is a rational number.
B. The answer nine square root of twelve is irrational because the sum of a rational number and irrational number is an irrational number.
C. The answer seven square root of three plus six is rational because the sum of a rational number and irrational number is a rational number.
D.The answer seven square root of three plus six is irrational because the sum of a rational number and irrational number is an irrational number.

Answer 1

Option D

Explanation:

Rational number is a number which can be expressed in the form
`(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
`(p)/(q)` and have a non-repeating, non-terminating decimal.

`7√(3)+2√(9)= 7√(3)+2*3=7√(3)+6`

Square root of 9 is 3 as
`3^(2)=3* 3 =9`

Here,
`7√(3)` is an irrational number as
`√(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

Answer 2

Option D. is correct.

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.