3 to the power 1/2 times 9 to the power 1/2

To solve \( 3^{\frac{1}{2}} \times 9^{\frac{1}{2}} \), we can follow these steps:

1. Recall that raising a number to the power of \(\frac{1}{2}\) is the same as taking its square root. So,
   \[
   3^{\frac{1}{2}} = \sqrt{3} \quad \text{and} \quad 9^{\frac{1}{2}} = \sqrt{9}
   \]
   
2. The square root of 9 is 3, so:
   \[
   9^{\frac{1}{2}} = 3
   \]
   
3. Now, multiply the two results together:
   \[
   \sqrt{3} \times 3 = 3\sqrt{3}
   \]

Thus, the result of \( 3^{\frac{1}{2}} \times 9^{\frac{1}{2}} \) is \( 3\sqrt{3} \).

Would you like more details or have any other questions?

Here are 5 related questions for further practice:
1. What is \( 4^{\frac{1}{2}} \times 16^{\frac{1}{2}} \)?
2. Simplify \( 2^{\frac{3}{2}} \times 8^{\frac{1}{2}} \).
3. Solve \( 5^{\frac{1}{2}} \times 25^{\frac{1}{2}} \).
4. What is \( 10^{\frac{1}{2}} \times 100^{\frac{1}{2}} \)?
5. Evaluate \( 7^{\frac{1}{2}} \times 49^{\frac{1}{2}} \).

**Tip**: Remember, powers of \(\frac{1}{2}\) represent square roots, and knowing your squares can help simplify expressions easily!

Learn how to solve the expression 3 to the power 1/2 times 9 to the power 1/2. This problem demonstrates the properties of exponents and square roots, showing how to simplify using key algebraic principles. Suitable for students in Grades 8-10.

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