contestada

Find the sum of \sqrt{4}√ ​4 ​ ​​ and 3\sqrt{9}3√ ​9 ​ ​​ in simplest form. also, determine whether the result is rational or irrational and explain your answer.

Respuesta :

tonb
√​4 + 3√​9 = 2+3*3  = 11.

This is a rational number, since the answer can be express as a fraction (e.g., 11/1).

This does not hold for square roots in general. For example √3 is irrational.

You can use the fact that if a square root contains only a squared quantity, then the root and the square will cancel out and that quantity will remain.

  • The sum of those given numbers in the simplest form is written as 11
  • The result is  rational.

What are rational numbers?


Those numbers who can be written as ratio of integers.

What are irrational numbers?

Those numbers who cannot be written as ratio of integers.

How to simplify given numbers and sum them?

[tex]\sqrt{4} = \sqrt{2^2} = 2\\\\3\sqrt{9} = 3 \times \sqrt{3^2} = 3 \times 3 = 9\\\\Thus,\\\\\sqrt{4} + 3\sqrt{9} = 2 + 9 = 11[/tex]

Since we can write 11  as 11:1 or 11/1, thus it is expressible as ratio of two integers, thus being a rational number.

Thus,

  • The sum of those given numbers in the simplest form is written as 11
  • The result is  rational.

Learn more about rational and irrational numbers here:

https://brainly.com/question/2563850