Question

which one is rational and which one is irrational:
square root of 25
0.66...
square root of 11
4/7
Answer
which ones are rational
Answer
convert .121212... into a fully simplified fraction
Answer
convert 0.5555... to a fraction
Answer
evaluate: 8 x 8 - 6 x 2
Answer
evaluate: -4/2^2 - (7-4)
Answered by GPT 3.5
The square root of 25 is rational because it is a whole number (5) which can be expressed as a fraction (5/1).

The number 0.66... is rational because it can be expressed as a fraction. To convert the repeating decimal to a fraction, we set it as x = 0.66... and multiply both sides by 100, which gives 100x = 66.66.... Subtracting x from both sides, we get 99x = 66. Simplifying, x = 66/99 and further reducing the fraction gives x = 2/3. Therefore, 0.66... is rational.

On the other hand, the square root of 11 is irrational because it cannot be expressed as a fraction or an exact whole number. It is a non-repeating, non-terminating decimal.

Finally, 4/7 is rational because it can be expressed as a fraction.
Answered by GPT 3.5
The rational numbers among the given options are:

- The square root of 25 (5) is rational.
- The number 0.66... can be expressed as the fraction 2/3, making it rational.
- 4/7 is also rational since it can be expressed as a fraction.

So, the square root of 11 is the only number in the given options that is irrational.
Answered by GPT 3.5
To convert the repeating decimal 0.121212... to a simplified fraction, we can set it as x = 0.121212... and multiply both sides by 100, which gives 100x = 12.121212... Next, we subtract x from both sides, which gives 99x = 12. Simplifying, we find that x = 12/99.

To simplify this fraction further, we can divide both the numerator and the denominator by their greatest common divisor, which is 3. Dividing 12 and 99 by 3 yields the simplified fraction 4/33. Therefore, the repeating decimal 0.121212... can be expressed as the simplified fraction 4/33.
Answered by GPT 3.5
To convert the repeating decimal 0.5555... to a fraction, we can set it as x = 0.5555... and multiply both sides by 10, which gives 10x = 5.5555...

Next, we subtract x from both sides, which gives 9x = 5.

Simplifying, we find that x = 5/9.

Therefore, the repeating decimal 0.5555... can be expressed as the fraction 5/9.
Answered by GPT 3.5
To evaluate the expression 8 x 8 - 6 x 2, we follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

First, we perform the multiplication: 8 x 8 = 64 and 6 x 2 = 12.

Now, we substitute these values back into the expression:

64 - 12 = 52.

Therefore, the evaluation of 8 x 8 - 6 x 2 is equal to 52.
Answered by GPT 3.5
To evaluate the expression -4/2^2 - (7-4), we follow the order of operations.

First, we evaluate the exponent:

2^2 = 2 x 2 = 4.

Now, let's substitute this value back into the expression:

-4/4 - (7-4).

Next, we simplify the parentheses:

-4/4 - 3.

Now, we perform the division:

-1 - 3.

Finally, we perform the subtraction:

-1 - 3 = -4.

Therefore, the evaluation of -4/2^2 - (7-4) is equal to -4.