Simplifying (3 root 3)(2 root 2)

To simplify the expression (3 root 3)(2 root 2), we can follow a few steps. Let's break it down step by step:

Step 1: Understand the concept of square roots
- A square root of a number is a value that, when multiplied by itself, gives the original number.
- For example, the square root of 4 is 2 because 2 * 2 = 4.

Step 2: Simplify the square root of each number separately
- In the given expression, we have (3 root 3)(2 root 2).
- The square root of 3 can be simplified as root 3.
- Similarly, the square root of 2 can be simplified as root 2.

Step 3: Apply the distributive property
- Using the distributive property, we can multiply each term inside the parentheses separately.
- Multiplying 3 by 2 gives us 6.
- Multiplying root 3 by root 2 gives us root 6.
- Therefore, the expression simplifies to 6 root 6.

Final Answer: 6 root 6

In conclusion, the simplified form of the expression (3 root 3)(2 root 2) is 6 root 6.

(3+√3 )×(2+√2) = (3×2)+(3×√2)+(√3×2)+(√3×√2) = 6+3√2 +2√3+√6