Which of the following is irrational?(1 point)
Responses
3√4
Start Fraction Start Root 3 End Root over 4 End Fraction
52.781654292
52.781654292
−7837
negative 7 Start Fraction 8 over 37 End Fraction
3.6363636363636363...
3√4 is irrational because it involves taking the cube root of 4, which is not a perfect cube.
52.781654292 is rational because it is a finite decimal.
−7837 is rational because it is a whole number.
3.6363636363636363... is rational because it is a repeating decimal.
Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
Responses
6.4
6.4
8.4
8.4
9.8
9.8
7.1
To estimate the value of 6×2–√, we first calculate the square root of 2. √2 is approximately 1.41.
Next, we multiply 6 by 1.41 and subtract it from 2.
6 × 1.41 = 8.46
2 - 8.46 = -6.46
Based on this calculation, the closest estimate from the given choices would be -6.46. However, none of the provided responses match this estimate.
Which statement is true about the square root of 28?(1 point)
Responses
It is between 6 and 7, probably closer to 6.
It is between 6 and 7, probably closer to 6.
It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 5.
It is between 5 and 6, probably closer to 5.
It is between 4 and 5, probably closer to 5.
To determine the statement that is true about the square root of 28, we can calculate an approximation.
The square root of 28 is approximately 5.29, which is between 5 and 6.
Therefore, the statement "It is between 5 and 6, probably closer to 5" is true for the square root of 28.
Which of the following is irrational?(1 point)
Responses
52.781654292
52.781654292
−7837
negative 7 Start Fraction 8 over 37 End Fraction
3√4
Start Fraction Start Root 3 End Root over 4 End Fraction
3.6363636363636363...
3.6363636363636363...
To determine which of the given options is irrational, we need to understand what an irrational number is. An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers.
Let's evaluate each option to determine if it is irrational:
1. 3√4: To find out if this is irrational, we need to simplify the expression. The cube root of 4 (√4) is equal to 2. Therefore, 3√4 = 3 * 2 = 6, which is a rational number.
2. 52.781654292: This is a decimal number, but it is not possible to determine if it is rational or irrational without more information. If the decimal part repeats or terminates, then it is rational. If it continues indefinitely without a pattern, then it is irrational. Please provide more information if applicable.
3. -7837: This is an integer, and all integers are rational numbers. Therefore, -7837 is rational.
4. 3.6363636363636363...: This decimal representation shows a repeating pattern of 36. If we convert it into a fraction, it can be written as 36/9 = 4. Therefore, 3.6363636363636363... is a rational number.
Based on the given options, none of them are irrational numbers.