Simplify the expression (square root 100 over 49)
a. 10 over 7
b. 17
c. 5 over 7***
d. 20 over 7
which sum will be irrational?
a. 3+2
b. square root 19 + 7 over 2
c. 18 over 3 + 11 over 10,000**
d. -6 + (-3.251)
which product will be rational
_
a. 17.12 * 33
b. square root 3 * square root 9
c. 4 * pie ***
d. -sqaure 20 * 15
I believe √100 = 10, not 5
anything that is only concerned with integers and fractions is rational.
√19 is irrational
nope
pi is irrational
the √ values are irrational
only (a) is rational
I think you have some reviewing to do...
To simplify the expression (square root 100 over 49), we need to simplify both the numerator and denominator separately and then divide them.
First, simplify the numerator by taking the square root of 100. The square root of 100 is 10.
Next, simplify the denominator by taking the square root of 49. The square root of 49 is 7.
Now we have (10 over 7).
Therefore, the simplified expression is 10 over 7. Option a is the correct answer.
For determining which sum will be irrational, it's important to recall that an irrational number is a number that cannot be written as a fraction or a terminating decimal.
Let's examine each option:
a. 3 + 2: This sum is 5, which can be written as the fraction 5 over 1. Therefore, it is rational.
b. square root 19 + 7 over 2: Here, we have an irrational number (square root 19) plus a rational number (7 over 2). Adding the two does not change the irrationality of square root 19. Therefore, it is irrational.
c. 18 over 3 + 11 over 10,000: This sum simplifies to 6 + 0.0011, which can be written as the fraction 60011 over 10,000. Therefore, it is rational.
d. -6 + (-3.251): This sum is -9.251, which can be written as the fraction -9251 over 1000. Therefore, it is rational.
Thus, option b, "square root 19 + 7 over 2," is the correct answer.
To determine which product will be rational, remember that a rational number can be written as a fraction or a terminating decimal.
Let's analyze each option:
a. 17.12 * 33: This product is 565.76, which can be written as the fraction 56576 over 100. Therefore, it is rational.
b. square root 3 * square root 9: The square root of 3 times the square root of 9 is the square root of 27. Since the square root of 27 cannot be written as a fraction or a terminating decimal, it is irrational.
c. 4 * pie: Here, the value of pie is an irrational number. However, when multiplied by 4, it remains irrational. Therefore, it is irrational.
d. -square root 20 * 15: This product simplifies to -square root 300. Similar to option b, the square root of 300 cannot be written as a fraction or a terminating decimal. Therefore, it is irrational.
Therefore, the only rational product is option a, "17.12 * 33."