What is the square root of 80 in simplified radical form?
sqrt 80 = sqrt (16*5) = 4 sqrt 5
To simplify the square root of 80, start by factoring 80 into its prime factors:
80 = 2 * 2 * 2 * 2 * 5
Now, we can write the square root of 80 as the square root of each factor multiplied together:
sqrt 80 = sqrt (2 * 2 * 2 * 2 * 5)
Next, we can simplify the square root of each perfect square (2 * 2 = 4) to get:
sqrt 80 = sqrt (4 * 4 * 5)
Since the square root of 4 is 2, we can simplify further:
sqrt 80 = 2 * 2 * sqrt 5
This can be written as:
sqrt 80 = 4 sqrt 5
Therefore, the square root of 80 in simplified radical form is 4 sqrt 5.
To find the square root of 80 in simplified radical form, we start by looking for perfect square factors of 80.
The prime factorization of 80 is 2^4 * 5.
Since 16 is a perfect square and a factor of 80, we can rewrite the square root of 80 as the square root of (16 * 5).
Using the property of square roots, we can split the square root of a product into the product of the square roots of each factor.
So, the square root of (16 * 5) becomes the square root of 16 multiplied by the square root of 5.
The square root of 16 is 4, as it is a perfect square.
Therefore, the simplified radical form of the square root of 80 is 4 * sqrt(5).