Final answer:
To simplify the expression (√21 √14 - 2√35) √7 / (7) √20, start by simplifying the square roots. Multiply the coefficients outside the square roots and simplify the numbers inside the square roots. The simplified expression is 3 √7 - 2√5 / 7 √5.
Step-by-step explanation:
To simplify the expression, (√21 √14 - 2√35) √7 / (7) √20, we can start by simplifying the square roots. √21 can be written as √(3 x 7) and √14 can be written as √(2 x 7). Similarly, √35 can be written as √(5 x 7) and √20 can be written as √(2 x 2 x 5).
After simplification, the expression becomes (√3 √7 - 2√(5x7)) √7 / (7) √(2x2x5).
Next, we can simplify the expression further by multiplying the coefficients outside the square roots. The expression becomes 3 √7 - 2√(35) / 7 √(20).
Finally, we can further simplify the expression by dividing the numbers inside the square roots. √35 can be written as √(5 x 7), which simplifies to √5 √7. Similarly, √20 can be written as √(2 x 2 x 5), which simplifies to 2 √5.
Therefore, the simplified expression is 3 √7 - 2√5 / 7 √5.