2√50*3√21/5√2*7√42
To simplify this expression, we can start by simplifying each of the square roots and then multiplying the resulting values together.
√50 = √(25 * 2) = 5√2
√21 remains the same.
√2 remains the same.
√42 = √(21 * 2) = √21 * √2 = √21√2 = 3√2
Now, we can substitute these simplified values back into the expression:
(2√50 * 3√21) / (5√2 * 7√42)
= (2(5√2) * 3√21) / (5√2 * 7(3√2))
= (10√2 * 3√21) / (5√2 * 21√2)
= (30√2√21) / (5√2√2 * 21)
= (30√2√21) / (5 * 21)
= (30√2√21) / 105
Since √2√21 = √(2 * 21) = √42, the final simplified expression is:
= (30√42) / 105
Therefore, the simplified expression is (30√42) / 105.
To simplify the expression (2√50 * 3√21) / (5√2 * 7√42), we can perform the following steps:
Step 1: Simplify each square root individually.
√50 = √(25 * 2) = 5√2
√21 = √(7 * 3) = √7√3
√2 = √2
√42 = √(6 * 7) = √6√7
Step 2: Substitute the simplified square roots into the entire expression.
(2 * 5√2 * 3√7√3) / (5√2 * 7√6√7)
Step 3: Cancel out common factors between the numerator and denominator.
The denominator has a 5, and the numerator has a 2 and a √2 that can be cancelled out.
(1 * √2 * 3√7√3) / (1 * 7√6√7)
Step 4: Combine the remaining terms in the numerator and the denominator.
(3 * √(2 * 7) * √(3 * 7)) / (7 * √(6 * 7))
Step 5: Simplify the expressions inside the square roots.
(3 * √14 * √21) / (7 * √42)
Step 6: Combine the square roots in the numerator and the denominator.
√14 * √21 = √(14 * 21) = √294
√42 = √(6 * 7) = √42
The final simplified expression is:
(3 * √294) / (7 * √42)
To simplify the expression, we can combine the factors that have the same radical (square root or cube root). Let's simplify each term first.
√50 = √(25 * 2) = √25 * √2 = 5√2
√21 cannot be simplified further because 21 does not have any perfect square factors.
√2 cannot be simplified further because 2 does not have any perfect square factors.
√42 = √(7 * 6) = √7 * √6. However, 6 has a perfect square factor, 2: √6 = √(2 * 3) = √2 * √3. Therefore, √42 = √7 * √(2 * 3) = √7 * √2 * √3.
Now let's substitute these values back into the original expression:
2√50 * 3√21 / 5√2 * 7√42
= 2(5√2)(3√21) / (5√2)(7√42)
= (2 * 5 * 3 * √2 * √21) / (5 * 7 * √2 * √42)
= (30√2√21)/(35√2√42)
To simplify further, we can combine the factors that have the same radical:
(30 * √2 * √21)/(35 * √2 * √42)
= (30 * √2 * √21) / (35 * √2 * √42)
= (30 * √(2 * 21)) / (35 * √(2 * 42))
= (30 * √42) / (35 * √84)
Since both 42 and 84 can be simplified to perfect squares, we can further simplify:
= (30 * √7 * √6) / (35 * √(4 * 21))
= (30 * √7 * √2 * √3) / (35 * 2 * √21)
= (15 * √7 * √3) / (35 * √21)
= (15 * √7 * √3) / (35 * √(7 * 3))
= (15 * √7 * √3) / (35 * √(7) * √(3))
= (15 * √7 * √3) / (35 * √7 * √3)
The √7 and √3 cancel out, leaving us with:
= 15 / 35
= 3 / 7
Therefore, the simplified form of the expression is 3/7.