Question

Given the two expressions shown below:

square root of 4 plus square root of 25
square root of 4 plus square root of 2

Which statement best describes the two expressions?
a.) Both are rational.
b.) Both are irrational.
c.) A is rational, but B is irrational.
d.) A is irrational, but B is rational.

Answer 1

What say you? Do you know the square roots off the top of your head?

Answer 2

http://www.factmonster.com/ipka/A0876704.html

Answer 3

@tkhunny I know the first on is \[\sqrt{5}\] and the second is \[\sqrt{2} \]

Answer 4

No, that's not right. You should have lost the radicals.

\(\sqrt{4} = 2\)

Answer 5

@tkhunny so 2 and 5? so both are irrational? or just 5?

Answer 6

In A we have the square root of 4 and 25 added together... We first need to remember that rational numbers are numbers that are able to be turned to fractions where the numbers are whole numbers....and irrational numbers are numbers that can only stay in decimal form... so with that in check we can start figuring which is which...

so like you said we see that the sqrt of 4 is 2 now we can turn this into a fraction which is 2/1 and they are both whole numbers which makes the sqrt of 4 rational.... Now you know that the sqrt of 25 is 5 so would that be rational or irrational?

Answer 7

@563blackghost 5 is irrational

Answer 8

That is incorrect we are able to turn 5 into a fraction which is 5/1 and they are both whole numbers so it is rational....

Answer 9

\(\sqrt{25} = 5\) That's rational.

Answer 10

@563blackghost @tkhunny what are examples of irrational? So the answer would be A?

Answer 11

We can't choose an answer yet cause we need to determine if part B is rational or irrational... in the link I provided it shows examples of ration and irrational numbers

Answer 12

@563blackghost okay so 2 is irrational but I did \[\sqrt{5}\] in my calculator and got 2.236

Answer 13

Any repeating decimal is Rational (including "terminating", which can be thought of as repeating"0")

0.142857142857... = 1/7 Rational

The square root of 5 is NOT 2.236. That is just an approximation.

\(\sqrt{5} = 2.23606797749979...\) -- Irrational

Answer 14

@tkhunny okay!

Answer 15

When finding the sqrt of a number the outcome would not have the radical....\[\sqrt{25}=5\] as you can see the radical is gone for the outcome...

Answer 16

@563blackghost
A.) 2
B.) 5
so 5 is rational and 2 is irrational

Answer 17

switch A B so A.) 5 and B.) 2

Answer 18

\[A.\sqrt{4}+\sqrt{25}=2+5=7\]
For A the outcome of the sqrts is 2 for sqrt of 4 and 5 for sqrt of 25....... so since we got whole numbers from these two problems we know that part A is rational....

\[B.\sqrt{4}+\sqrt{2}=2+1.414213…=3.414213\]
For part B we have the sqrt of 2 which @tkhunny said is irrational meaning that all of part B is irrational since the outcome would have a decimal to it which is not repeating and cannot be turned into a fraction...

Answer 19

think of rational as " can be expressed as the ratio of whole numbers"
think about the square of whole numbers and the opposite the square root
now you have rt 2 rt 4 and rt 25
you do not need a calculator