Find the positive square roots of 5 to the power of 4 x 7 to the power of 2

To find the positive square root of \( 5^4 \times 7^2 \), we can proceed step by step:

### Step 1: Simplify the expression
First, evaluate the powers:
- \( 5^4 = 625 \)
- \( 7^2 = 49 \)

Thus, the expression becomes:
\[
625 \times 49
\]

### Step 2: Multiply the numbers
\[
625 \times 49 = 30,625
\]

### Step 3: Find the positive square root
Now, find the square root of 30,625:
\[
\sqrt{30,625} = 175
\]

So, the positive square root of \( 5^4 \times 7^2 \) is **175**.

Would you like more details or have any questions?

### Related Questions:
1. How would you find the negative square root of \( 5^4 \times 7^2 \)?
2. What is the square root of \( 5^6 \times 7^4 \)?
3. Can you break down \( 5^4 \times 7^2 \) into its prime factors and find the square root step by step?
4. How do you find the square root of a product involving more than two numbers?
5. What is the cube root of \( 5^4 \times 7^2 \)?

### Tip:
When simplifying square roots of products, you can often break them into smaller parts and simplify each one separately before multiplying the results.

Find the positive square roots of 5 to the power of 4 x 7 to the power of 2.

Discover how to find the positive square root of 5 to the power of 4 multiplied by 7 to the power of 2. This step-by-step guide explains exponentiation, multiplication, and square roots. Perfect for students in Grades 8-10.

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