Square Root Of 6072 In Simplest Radical Form
Simplify the square root of 6072 to its lowest radical form.ANSWER: 2√1518
2√1518 is in the lowest radical form.
Simplified Radical Form of √6072
One of the main facts used to simplify square roots is that the square root of a product is equal to the product of square roots: √(x×y) = √x×√y
Explanation:
When we find square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them.
Step 1: List Factors
To simplify √6072, we need to divide into factors.
√6072 = √2 x √2 x √2 x √3 x √11 x √23Step 2: List Perfect Squares
1 is a perfect square and divides 6072
4 is a perfect square and divides 6072
Step 3: Divide To Perfect Square
Divide 6072 by the largest perfect square you found in the previous step:
Step 4: Calculate The Square Root
Calculate the square root of the largest perfect square:
Final Step :
Put Steps 3 and 4 together to get the square root of 6072 in its simplest form: 2√1518
How do you simplify √6072
The general approach is to first check if it is a perfect square. If so, you have the answer. If it is not a perfect square, see if any of its factors are perfect squares, or can be combined to make square numbers.
Find the lowest prime number that can divide 6072. Divide 6072 repeatedly using the long division method till you reach 1.
A pair of factor 'twins' under a square root sign (radical) form a single factor outside of it.
Factors that do not have a twin remain under the radical. Multiply them back together and leave them in there.
So, the answer is 2√1518.
Simplified Decimal Form of √6072
The square root of 6072 is approximately 77.923 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √15 | Square root of 15 is the simplest radical form. | √3 x √5 |
| √10 | Square root of 10 is the simplest radical form. | √2 x √5 |
| √22 | Square root of 22 is the simplest radical form. | √2 x √11 |
| √736 | 4√46 | √2 x √2 x √2 x √2 x √2 x √23 |
| √256 | 16√1 | √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 |
| √158 | Square root of 158 is the simplest radical form. | √2 x √79 |
| √6118 | Square root of 6118 is the simplest radical form. | √2 x √7 x √19 x √23 |
| √4442 | Square root of 4442 is the simplest radical form. | √2 x √2221 |
| √1983 | Square root of 1983 is the simplest radical form. | √3 x √661 |