write the following in simplified radical form 3 sqrt 250
3(sqrt250)= 3*(sqrt 25)* (sqrt 10)
= 3 * 5 * (sqrt 10)
= 15 (sqrt 10)
To simplify the expression √250, we can break down 250 into its prime factors: 2 × 5 × 5 × 5.
We can now rewrite the expression as follows:
√250 = √(2 × 5 × 5 × 5)
Next, we group pairs of the same factors inside the radical:
√(2 × (5 × 5) × 5)
Since 5 × 5 simplifies to 25, the expression becomes:
√(2 × 25 × 5)
Further simplifying, we have:
√(50 × 5)
Which can be rewritten as:
√(50) × √(5)
Since √(50) simplifies to √(25 × 2), the expression becomes:
√(25 × 2) × √(5)
Simplifying √(25 × 2) gives us:
√(25) × √(2) × √(5)
Finally, we have:
5√(2) × √(5)
This is the simplified radical form of 3√250.
To simplify the radical expression 3√250, start by finding the prime factorization of 250:
250 = 2 × 5 × 5 × 5
Now, group the factors inside the radical sign in pairs, using the exponent rule of radicals:
3√(2 × (5 × 5 × 5))
Since there are three 5's, we can take one of them out of the radical:
3√(2 × 5 × 5 × √5)
Simplifying the square root under the radical:
3√(2 × 5 × 5√5)
Finally, simplify the expression:
3 × 5 × √(2 × 5√5)
15√(10√5)
Therefore, the simplified radical form of 3√250 is 15√(10√5).