Question

Упростить дробь 6√3*√3 ______ 3

Answer 1

$\frac{6\sqrt{3} *\sqrt{3}}{3} = \frac{6*3}{3} = 6$

Answer 2

To simplify the fraction, we'll start by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of the denominator is the same expression, but with the opposite sign between the terms (i.e., 3 becomes -3). This process eliminates the square root from the denominator.

Here's how it looks step by step:

Step 1: Multiply the numerator and denominator by the conjugate of the denominator (-3): (6√3 * √3) / 3 * (-3) / (-3)

Step 2: Simplify the expression in the numerator: (6√3 * √3) = 6 * (√3)^2 = 6 * 3 = 18

Step 3: Simplify the expression in the denominator: 3 * (-3) = -9

Now, the fraction becomes: 18 / -9

Step 4: Reduce the fraction to its simplest form: Divide both the numerator and denominator by their greatest common divisor (GCD), which is 9. 18 ÷ 9 = 2 -9 ÷ 9 = -1

The simplified fraction is: 2 / -1

However, it's common practice to express fractions with a negative sign in the numerator. So the final simplified fraction is: -2