Question

"Write down an irrational number that satisfies this inequality."

Answer 1

sqrt(26)

Explanation:

Irrational numbers can be the square root of any non-perfect square number.

there are many between 4 and 7

for instance sqrt(26), and we cant actually write out a value, we have to write sqrt of 26, or like 2pi, because the decimals go forever, we cant express that, but what makes them unique is that the decimals don't ever repeat. we can express 7.7777... as 7 with a bar on top, but you cant really express pi, while still being perfectly precise.

Answer 2

Explanation:

The limits are 16 and 49.

By that, I mean that if you choose any number which is not a perfect square (like 25 or 36), then take the square root of that number, it will be an irrantional number between 4 < m < 7

So look at 17 for example

The square root of 17 = √17

What does √17 = 4.123 as an approximation.

What about √(26)? The √(26) = 5.099 as an approximation.

You should show yourself that neither √15 nor √51 satisfies the inequality.