Divide: 48 × (√2 / 1) × 25√3 × 49√5 by 7√3 × 5√2.
Answer (2)
To solve this problem, we will perform the division step-by-step:
We need to divide the expression 48 × 1 2 × 25 3 × 49 5 by 7 3 × 5 2 .
First, let's simplify the expression:
Simplifying the numerator:
48 × 2 × 25 × 3 × 49 × 5
Combine like terms: 48 × 25 × 49 × 2 × 3 × 5
Calculate the numerical multiplication: 48 × 25 = 1200 and 1200 × 49 = 58800
Combine the square roots: 2 × 3 × 5 = 30
So, the numerator simplifies to: 58800 30
Simplifying the denominator:
7 3 × 5 2
Combine: 7 × 5 × 3 × 2
Calculate the numerical multiplication: 7 × 5 = 35
Combine the square roots: 3 × 2 = 6
So, the denominator simplifies to: 35 6
Perform the division:
35 6 58800 30
Divide the numbers: 35 58800 = 1680
For the square roots, use the property: 6 30 = 6 30 = 5
Thus, the final result is: 1680 5
Therefore, the result of the division is 1680 5 .
The division of the expression results in 1680√5 after simplifying both the numerator and the denominator. The numerator combines to 58800√30 and the denominator to 35√6. When dividing, the numerical part is simplified to 1680 and the square roots simplify to √5.
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