The product of a multiplication problem is 225−−−√ . What do you know about the factors?(1 point) Responses One factor is rational, but the other is irrational. One factor is rational, but the other is irrational. It cannot be predicted based on the information given. It cannot be predicted based on the information given. At least one factor is irrational because the product is irrational. At least one factor is irrational because the product is irrational. They are both rational because the product is rational.

Answer 1

The product of the multiplication problem is \( \sqrt{225} \).

Calculating the square root, we have:

\[ \sqrt{225} = 15 \]

Since 15 is a rational number, we can deduce the nature of the factors involved in the multiplication that yields this product.

For any two numbers \( a \) and \( b \) such that \( a \cdot b = 15 \):

• If both factors \( a \) and \( b \) were irrational, their product would also be irrational.
• If both factors were rational, their product would also be rational.
• If one factor is rational and the other is irrational, the product would be irrational as well.

Since the product \( 15 \) is rational, both factors must be rational or at least one must be rational. Therefore, the correct answer among your options is that:

They are both rational because the product is rational.

Answer 2

What type of number will the product of π and 34 be?(1 point) Responses a repeating decimal a repeating decimal a radical a radical an irrational number an irrational number a rational number

Answer 3

The product of \( \pi \) (which is an irrational number) and 34 (which is a rational number) can be examined as follows:

When you multiply a rational number (like 34) by an irrational number (like \( \pi \)), the result is always an irrational number. This is because there are no two rational numbers that can be multiplied together to result in an irrational number.

Thus, the correct answer is:

an irrational number.

Answer 4

What type of number will the product of π and 3/4 be?(1 point) Responses a repeating decimal a repeating decimal a radical a radical an irrational number an irrational number a rational number
thats what i meant

Answer 5

The product of \( \pi \) (an irrational number) and \( \frac{3}{4} \) (a rational number) is being considered here.

When you multiply a rational number by an irrational number, the result is always an irrational number.

Thus, the product of \( \pi \) and \( \frac{3}{4} \) will be:

an irrational number.

Answer 6

Charles, Zayeer, and Kali are trying to simplify 1,00023 . Charles says the correct simplification is 10 because 1,000=10⋅10⋅10 and 1,00023=10 . Zayeer says the correct simplification is 1,000 because 1,000=10⋅10⋅10→1,00023=10⋅10⋅10=1,000 . Kali says the correct simplification is 100 because 1,000=10⋅10⋅10→1,00023=10⋅10=100 . Who has the correct value?(1 point) Responses none of them none of them Kali Kali Zayeer Zayeer Charles

Answer 7

To simplify \( 1,000^{23} \), we can start with the expression \( 1,000 \) in terms of powers of 10:

\[ 1,000 = 10^3 \]

Now, substituting this back into the expression:

\[ 1,000^{23} = (10^3)^{23} \]

According to the power of a power property of exponents, we multiply the exponents:

\[ (10^3)^{23} = 10^{3 \cdot 23} = 10^{69} \]

Thus, \( 1,000^{23} \) simplifies to \( 10^{69} \), which is not one of the suggested simplifications.

Therefore, the correct conclusion is that:

none of them has the correct value.

Answer 8

simplify 243 3/5

Answer 9

To simplify \( 243 \frac{3}{5} \), you can convert the mixed number into an improper fraction. Here's how to do that:

1. Convert the whole number to a fraction: The whole number \( 243 \) can be expressed as \( \frac{243 \times 5}{5} = \frac{1215}{5} \).
2. Add the fractional part: Add the fraction \( \frac{3}{5} \) to this improper fraction:

\[ \frac{1215}{5} + \frac{3}{5} = \frac{1215 + 3}{5} = \frac{1218}{5} \]

So, the simplified form of \( 243 \frac{3}{5} \) as an improper fraction is:

\[ \frac{1218}{5} \]

If you prefer it as a decimal, you can also convert \( \frac{1218}{5} \) by dividing:

\[ 1218 \div 5 = 243.6 \]

Thus, \( 243 \frac{3}{5} \) can be expressed as either \( \frac{1218}{5} \) or \( 243.6 \).

Answer 10

can you simplify what you said

Answer 11

Sure! Here’s a simplified explanation of \( 243 \frac{3}{5} \):

1. Convert the mixed number \( 243 \frac{3}{5} \) into an improper fraction: \[ 243 \frac{3}{5} = \frac{243 \times 5 + 3}{5} = \frac{1215 + 3}{5} = \frac{1218}{5} \]

2. So, \( 243 \frac{3}{5} \) simplifies to \( \frac{1218}{5} \).

You can also express it as a decimal: \[ \frac{1218}{5} = 243.6 \]

Final result: \( 243 \frac{3}{5} = \frac{1218}{5} \) or \( 243.6 \).