Find the sum of 5, square root of, 9, end square root5 9 ​ and 4, square root of, 4, end square root4 4 ​ in simplest form. Also, determine whether the result is rational or irrational and explain your answer. Answer

Answer 1

To find the sum of \( 5 \sqrt{9} + 4 \sqrt{4} \), let's calculate each term first.

1. Calculate \( \sqrt{9} \): \[ \sqrt{9} = 3 \] So, \( 5 \sqrt{9} = 5 \times 3 = 15 \).

2. Calculate \( \sqrt{4} \): \[ \sqrt{4} = 2 \] So, \( 4 \sqrt{4} = 4 \times 2 = 8 \).

Now, we can sum both results: \[ 5 \sqrt{9} + 4 \sqrt{4} = 15 + 8 = 23. \]

Thus, the sum in simplest form is: \[ \boxed{23}. \]

Next, to determine whether the result is rational or irrational:

• A rational number is any number that can be expressed as the quotient or fraction of two integers (where the denominator is not zero).
• An irrational number, on the other hand, cannot be expressed as such a fraction.

Since \( 23 \) can be expressed as \( \frac{23}{1} \), it is a rational number.

Therefore, the final conclusion is that the result \( 23 \) is rational.