To solve the expression 8 raised to the power 1/2 multiplied by 7 raised to the power 1/2, we can break it down step by step.

Step 1: Simplify each expression individually.
- 8 raised to the power 1/2 is equivalent to the square root of 8. The square root of 8 can be written as √8 or 8^(1/2).
- 7 raised to the power 1/2 is equivalent to the square root of 7. The square root of 7 can be written as √7 or 7^(1/2).

Step 2: Multiply the simplified expressions.
- (√8) * (√7) = (√(8 * 7)) = √56 = 56^(1/2)

Step 3: Simplify the final expression.
- √56 is an irrational number, meaning it cannot be expressed as a simple fraction or whole number. However, we can approximate it as 7.4833.

Therefore, 8^(1/2) multiplied by 7^(1/2) is approximately equal to 7.4833.

In summary:
- 8 raised to the power 1/2 is equivalent to the square root of 8, written as √8 or 8^(1/2).
- 7 raised to the power 1/2 is equivalent to the square root of 7, written as √7 or 7^(1/2).
- (√8) * (√7) is equal to √(8 * 7) or √56.
- √56 is an irrational number, approximately equal to 7.4833.