1224√3300√

Answer 1

To evaluate \( 1224 \sqrt{3300} \), we first simplify \( \sqrt{3300} \).

1. Factor \( 3300 \): \[ 3300 = 33 \times 100 = 33 \times 10^2 \] \[ 33 = 3 \times 11 \quad \text{and} \quad 100 = 10^2 = (10)^2 \] Thus, we can write: \[ 3300 = 3 \times 11 \times 100 = 3 \times 11 \times 10^2 \]

2. Taking the square root: \[ \sqrt{3300} = \sqrt{3 \times 11 \times 100} = \sqrt{3 \times 11} \times \sqrt{100} = 10 \sqrt{33} \]

3. Substitute back into the expression: \[ 1224 \sqrt{3300} = 1224 \times 10 \sqrt{33} \] \[ = 12240 \sqrt{33} \]

Thus, the value of \( 1224 \sqrt{3300} \) simplifies to: \[ \boxed{12240 \sqrt{33}} \]

Answer 2

12/sqrt24 divided by 3/sqrt300

Answer 3

To solve the expression \( \frac{12}{\sqrt{24}} \div \frac{3}{\sqrt{300}} \), we can first rewrite the division as a multiplication by the reciprocal:

\[ \frac{12}{\sqrt{24}} \div \frac{3}{\sqrt{300}} = \frac{12}{\sqrt{24}} \times \frac{\sqrt{300}}{3} \]

Now, we can multiply the fractions:

\[ = \frac{12 \cdot \sqrt{300}}{3 \cdot \sqrt{24}} \]

Next, simplify the fraction:

\[ = \frac{12}{3} \cdot \frac{\sqrt{300}}{\sqrt{24}} = 4 \cdot \frac{\sqrt{300}}{\sqrt{24}} = 4 \cdot \sqrt{\frac{300}{24}} \]

Now, simplify the fraction inside the square root:

\[ \frac{300}{24} = \frac{300 \div 12}{24 \div 12} = \frac{25}{2} \]

So, we have:

\[ \sqrt{\frac{300}{24}} = \sqrt{\frac{25}{2}} = \frac{\sqrt{25}}{\sqrt{2}} = \frac{5}{\sqrt{2}} \]

Now substituting back, we have:

\[ 4 \cdot \frac{5}{\sqrt{2}} = \frac{20}{\sqrt{2}} \]

For final simplification, we can rationalize the denominator:

\[ \frac{20}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{20\sqrt{2}}{2} = 10\sqrt{2} \]

Thus, the final result is:

\[ \boxed{10\sqrt{2}} \]

Answer 4

What is the quotient of the following expression? State the answer in simplest radical form. Rationalize the denominator if necessary.

12/24√3/300√

Answer 5

To calculate the quotient of the expression \(\frac{12}{24\sqrt{3}} \div \frac{300}{\sqrt{}} \), we will first clarify the expression as follows:

\[ \frac{12}{24\sqrt{3}} \div \frac{300}{\sqrt{}} \equiv \frac{12}{24\sqrt{3}} \div \frac{300}{1} = \frac{12}{24\sqrt{3}} \times \frac{1}{300} \]

We can rewrite this as:

\[ \frac{12 \cdot 1}{24\sqrt{3} \cdot 300} \]

Now, we can simplify the numerator and denominator:

1. Simplify \( \frac{12}{24} \): \[ \frac{12}{24} = \frac{1}{2} \]

Now, we substitute this back into the expression:

\[ = \frac{1}{2\sqrt{3} \cdot 300} = \frac{1}{600\sqrt{3}} \]

2. Rationalize the denominator: To rationalize the denominator, multiply the numerator and the denominator by \(\sqrt{3}\):

\[ \frac{1 \cdot \sqrt{3}}{600\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{3}}{600 \cdot 3} = \frac{\sqrt{3}}{1800} \]

Thus, the final answer in simplest radical form is:

\[ \boxed{\frac{\sqrt{3}}{1800}} \]

Answer 6

What is the quotient of the following expression? State the answer in simplest radical form. Rationalize the denominator if necessary.

12/√24/3/√300

Answer 7

To find the quotient of the expression \(\frac{12}{\sqrt{24}} \div \frac{3}{\sqrt{300}}\), we first rewrite the division as multiplication by the reciprocal:

\[ \frac{12}{\sqrt{24}} \div \frac{3}{\sqrt{300}} = \frac{12}{\sqrt{24}} \times \frac{\sqrt{300}}{3} \]

Now we can combine the two fractions:

\[ = \frac{12 \cdot \sqrt{300}}{3 \cdot \sqrt{24}} \]

Next, we simplify:

1. Reduce \( \frac{12}{3} \): \[ \frac{12}{3} = 4 \]

So our expression becomes:

\[ = \frac{4\sqrt{300}}{\sqrt{24}} \]

Now, let's simplify \(\frac{\sqrt{300}}{\sqrt{24}}\):

\[ \frac{\sqrt{300}}{\sqrt{24}} = \sqrt{\frac{300}{24}} \]

Now we simplify \(\frac{300}{24}\):

\[ \frac{300}{24} = \frac{300 \div 12}{24 \div 12} = \frac{25}{2} \]

So we have:

\[ \sqrt{\frac{300}{24}} = \sqrt{\frac{25}{2}} = \frac{\sqrt{25}}{\sqrt{2}} = \frac{5}{\sqrt{2}} \]

Now substituting back, we get:

\[ = 4 \cdot \frac{5}{\sqrt{2}} = \frac{20}{\sqrt{2}} \]

Next, we rationalize the denominator:

\[ \frac{20}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{20\sqrt{2}}{2} = 10\sqrt{2} \]

Thus, the final answer in simplest radical form is:

\[ \boxed{10\sqrt{2}} \]