Question

Complete the expression adding the radicals.
10 sqrt(5) + 3sqrt(45) =13 sqrt ?
Answer
Complete the expression adding the radicals.

10 sqrt(5) + 3sqrt(45) = ?
Answer
Complete the expression adding the radicals.

9 sqrt(5) + 3sqrt(45) = ?
Answer

Complete the expression adding the radicals.

5 sqrt(5) + 3sqrt(45) = ?
Answer

Complete the expression adding the radicals.

4 sqrt(5) + 3sqrt(45) = ?
Answered by GPT-4o mini
To simplify the expression \(10\sqrt{5} + 3\sqrt{45}\) and express it in the form \(13\sqrt{x}\), we first simplify \(3\sqrt{45}\).

First, we can simplify \(\sqrt{45}\):

\[
\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

Now we can substitute this back into the expression:

\[
3\sqrt{45} = 3(3\sqrt{5}) = 9\sqrt{5}
\]

Now we can add this to \(10\sqrt{5}\):

\[
10\sqrt{5} + 9\sqrt{5} = (10 + 9)\sqrt{5} = 19\sqrt{5}
\]

To have it in the form \(13\sqrt{x}\), we can express \(19\sqrt{5}\) as follows:

\[
19\sqrt{5} = 13\sqrt{x}
\]

To find \(x\), we can set the coefficients equal to each other:

\[
19\sqrt{5} = 13\sqrt{x}
\]

If we divide both sides by 13, we get:

\[
\sqrt{x} = \frac{19}{13} \sqrt{5}
\]

Squaring both sides gives us:

\[
x = \left(\frac{19}{13}\right)^2 \cdot 5
\]

Calculating \(\left(\frac{19}{13}\right)^2\):

\[
\left(\frac{19}{13}\right)^2 = \frac{361}{169}
\]

Now substituting back:

\[
x = \frac{361}{169} \cdot 5 = \frac{1805}{169}
\]

Thus, the completed expression is:

\[
10 \sqrt{5} + 3 \sqrt{45} = 19\sqrt{5} = 13\sqrt{\frac{1805}{169}}
\]

In conclusion, the answer is:

\[
x = \frac{1805}{169}
\]

So \(10\sqrt{5} + 3\sqrt{45} = 13\sqrt{\frac{1805}{169}}\).
Answered by GPT-4o mini
To complete the expression \(10\sqrt{5} + 3\sqrt{45}\), we first need to simplify \(3\sqrt{45}\).

1. **Simplify \(\sqrt{45}\)**:
\[
\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

2. **Substituting back**:
\[
3\sqrt{45} = 3(3\sqrt{5}) = 9\sqrt{5}
\]

3. **Now add the terms together**:
\[
10\sqrt{5} + 9\sqrt{5} = (10 + 9)\sqrt{5} = 19\sqrt{5}
\]

Therefore, the final expression is:

\[
10\sqrt{5} + 3\sqrt{45} = 19\sqrt{5}
\]
Answered by GPT-4o mini
To complete the expression \(9\sqrt{5} + 3\sqrt{45}\), we first simplify \(3\sqrt{45}\).

1. **Simplify \(\sqrt{45}\)**:
\[
\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

2. **Substituting back into the expression**:
\[
3\sqrt{45} = 3(3\sqrt{5}) = 9\sqrt{5}
\]

3. **Now add the terms together**:
\[
9\sqrt{5} + 9\sqrt{5} = (9 + 9)\sqrt{5} = 18\sqrt{5}
\]

Therefore, the final expression is:

\[
9\sqrt{5} + 3\sqrt{45} = 18\sqrt{5}
\]
Answered by GPT-4o mini
To complete the expression \(5\sqrt{5} + 3\sqrt{45}\), we first simplify \(3\sqrt{45}\).

1. **Simplify \(\sqrt{45}\)**:
\[
\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

2. **Substituting back into the expression**:
\[
3\sqrt{45} = 3(3\sqrt{5}) = 9\sqrt{5}
\]

3. **Now add the terms together**:
\[
5\sqrt{5} + 9\sqrt{5} = (5 + 9)\sqrt{5} = 14\sqrt{5}
\]

Therefore, the final expression is:

\[
5\sqrt{5} + 3\sqrt{45} = 14\sqrt{5}
\]
Answered by GPT-4o mini
To calculate the expression \( 4\sqrt{5} + 3\sqrt{45} \), we first need to simplify \( 3\sqrt{45} \).

1. **Simplify \(\sqrt{45}\)**:
\[
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}
\]

2. **Substituting this back into the expression**:
\[
3\sqrt{45} = 3(3\sqrt{5}) = 9\sqrt{5}
\]

3. **Now add the terms together**:
\[
4\sqrt{5} + 9\sqrt{5} = (4 + 9)\sqrt{5} = 13\sqrt{5}
\]

Therefore, the final expression is:
\[
4\sqrt{5} + 3\sqrt{45} = 13\sqrt{5}
\]