Question

Blank radical 5 + 3 radical 45 equals 13 radical what

Answer 1

To solve the expression \( \sqrt{5} + 3\sqrt{45} = 13 \sqrt{x} \), we first simplify the term \( 3\sqrt{45} \).

We know that \( \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \).

Now, substituting this back we have:

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

Now, we can combine terms on the left side of the equation:

\[
\sqrt{5} + 9\sqrt{5} = 10\sqrt{5}
\]

Now we rewrite the equation:

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

To solve for \( x \), we can first isolate \( \sqrt{x} \):

\[
\sqrt{x} = \frac{10\sqrt{5}}{13}
\]

Now, to eliminate the square root, we square both sides:

\[
x = \left( \frac{10\sqrt{5}}{13} \right)^2 = \frac{100 \cdot 5}{169} = \frac{500}{169}
\]

Thus, the solution is:

\[
\boxed{\frac{500}{169}}
\]