Simplify the square root.
2 square root 50. What are the steps to simplify this problem.
50 = 25*2 = 5^2 * 2
√50 = 5√2
2√50 = 10√2
2√50
= 2√25√2
= 2(5)√2
= 10√2
Well, to simplify the square root of 2 times the square root of 50, we can use the product property of square roots.
First, we can break down the number inside the square root. The square root of 50 can be simplified as the square root of 25 times 2.
The square root of 25 is 5, so we can rewrite the expression as 2 times 5 times the square root of 2.
Finally, multiplying 2 and 5 gives us 10, so the simplified expression is 10 times the square root of 2.
To simplify the square root of 2 times the square root of 50, you can follow these steps:
Step 1: Start by breaking down the number inside the square root into its prime factorization. For the number 50, the prime factors are 2 x 5 x 5.
Step 2: Rewrite the square root expression using the prime factors. So, √(50) becomes √(2 x 5 x 5).
Step 3: Separate the prime factors into two separate square roots. The square root of 2 is left outside the radical symbol, while the prime factors with an even number of occurrences (two 5s here) are placed inside the radical symbol. So, the expression becomes √(2) x √(5 x 5).
Step 4: Simplify each square root separately. The square root of 2 cannot be simplified any further, while the square root of 5 x 5 is just 5. Therefore, the expression simplifies to 2√(5).
So, the simplified form of √(2 x 50) is 2√(5).