Simplify.
75
square root
√75 = √(25*3) = √25 * √3 = 5√3
To simplify the square root of 75, we can break down 75 into its prime factors.
The prime factorization of 75 can be written as 3 * 5^2.
Now, we can simplify the square root of 75.
√75 = √(3 * 5^2)
Taking the square root of 5^2 simplifies to 5.
So, √(3 * 5^2) = 5√3
Therefore, the simplified form of the square root of 75 is 5√3.
To simplify the square root of 75, we can break down the number into its prime factors and simplify the square root expression using the properties of square roots.
1. Prime factorization of 75:
We start by finding the prime factors of 75. The prime factors of 75 are 3 and 5 because 3 * 5 = 15, and 15 * 5 = 75.
Therefore, the prime factorization of 75 is 3 * 5 * 5.
2. Simplifying the square root expression:
We can simplify the square root of 75 by grouping the prime factors under the square root sign.
√(3 * 5 * 5)
With the properties of square roots, we can separate the square root of a product into the square roots of the individual factors.
√3 * √5 * √5
The square root of 5 * 5 is simply 5.
√3 * 5
Thus, the simplified form of the square root of 75 is 5√3.