2 square root 3(square root of 7- square root of 3)
To simplify the expression, we'll start by distributing the 2 to the terms inside the parentheses.
2(square root of 3)(square root of 7 - square root of 3)
Next, consider the product of two square roots. The square root of a number can be written as the number raised to the power of (1/2). So, we have:
2 * (3^(1/2)) * ((7^(1/2)) - (3^(1/2)))
Simplifying further, we can rewrite the expression as:
2 * √3 * (√7 - √3)
Now let's multiply the terms inside the parentheses using the distributive property:
2 * √3 * √7 - 2 * √3 * √3
Simplifying the second term:
2 * √3 * √7 - 2 * 3
2 * √3 * √7 - 6
Finally, multiplying the remaining terms:
2√21 - 6
Therefore, the simplified expression is 2√21 - 6.