Square Root Of 3888 In Simplest Radical Form
Simplify the square root of 3888 to its lowest radical form.ANSWER: 36√3
36√3 is in the lowest radical form.
Simplified Radical Form of √3888
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 √3888, we need to divide into factors.
√3888 = √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 3888
4 is a perfect square and divides 3888
9 is a perfect square and divides 3888
16 is a perfect square and divides 3888
36 is a perfect square and divides 3888
81 is a perfect square and divides 3888
144 is a perfect square and divides 3888
324 is a perfect square and divides 3888
1296 is a perfect square and divides 3888
Step 3: Divide To Perfect Square
Divide 3888 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 3888 in its simplest form: 36√3
How do you simplify √3888
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 3888. Divide 3888 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 36√3.
Simplified Decimal Form of √3888
The square root of 3888 is approximately 62.354 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √41 | Square root of 41 is the simplest radical form. | √41 |
| √62 | Square root of 62 is the simplest radical form. | √2 x √31 |
| √4 | 2√1 | √2 x √2 |
| √907 | Square root of 907 is the simplest radical form. | √907 |
| √110 | Square root of 110 is the simplest radical form. | √2 x √5 x √11 |
| √355 | Square root of 355 is the simplest radical form. | √5 x √71 |
| √9158 | Square root of 9158 is the simplest radical form. | √2 x √19 x √241 |
| √3856 | 4√241 | √2 x √2 x √2 x √2 x √241 |
| √2551 | Square root of 2551 is the simplest radical form. | √2551 |