Question

Simplify the expression 45g3h6−−−−−−√ by answering each question and checking your answer before moving to the next step.

Step 1: Rewrite 45−−√ as the product of two square root factors, one of which is a perfect square. Then simplify the expression.

Use the keypad to enter the answers in the boxes.

45−−√=
=

Answer 1

To simplify \( \sqrt{45} \), we can rewrite it as the product of two square root factors, one of which is a perfect square.

Step 1: First, we notice that \( 45 = 9 \times 5 \). Here, \( 9 \) is a perfect square.

Thus, we can rewrite \( \sqrt{45} \) as:
\[
\sqrt{45} = \sqrt{9 \times 5}
\]

Step 2: Now, we apply the property of square roots that states \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \):

\[
\sqrt{45} = \sqrt{9} \times \sqrt{5}
\]

Finally, we simplify \( \sqrt{9} \):
\[
\sqrt{9} = 3
\]

So we have:
\[
\sqrt{45} = 3\sqrt{5}
\]

To summarize:
\[
\sqrt{45} = 3\sqrt{5}
\]

If you need this in the format of:

- \( 45 \sqrt{=}\)
- \( 3\sqrt{5} \)

then we have:
\[
\sqrt{45} = 3 \sqrt{5}
\]

Let me know if you want to proceed to the next step!