Question

A garden is √300 feet by √75 feet. What is the area in simplest radical form? (1 point)

Answer 1

To find the area of the garden, we need to multiply the two dimensions together:

\[
\text{Area} = \sqrt{300} \times \sqrt{75}
\]

Using the property of square roots that \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \), we can combine the square roots:

\[
\text{Area} = \sqrt{300 \times 75}
\]

Now, we can calculate the product inside the square root:

\[
300 \times 75 = 22500
\]

Next, we need to find the square root of \( 22500 \). We can simplify this step by first factorizing the number:

\[
22500 = 225 \times 100
\]

Now we can take the square root:

\[
\sqrt{22500} = \sqrt{225 \times 100} = \sqrt{225} \times \sqrt{100} = 15 \times 10 = 150
\]

Thus, the area of the garden in simplest radical form is:

\[
\boxed{150}
\]