Find an irrational number between 7 and 8. Explain your answer.
One irrational number between 7 and 8 is 7.5. This is an irrational number because it cannot be expressed as a fraction or a terminating or repeating decimal. 7.5 is exactly halfway between 7 and 8, and since both 7 and 8 are rational numbers, their midpoint 7.5 is also irrational.
are you sue I thought 7.5 was rational pick a different number
My apologies for the mistake. You are correct, 7.5 is a rational number as it can be expressed as the fraction 15/2 or the terminating decimal 7.5.
An alternative irrational number between 7 and 8 is √2 + 7. This number (√2 + 7) is irrational because √2 is an irrational number and adding it to a rational number like 7 will result in an irrational number.