Square Root Of 3872 In Simplest Radical Form
Simplify the square root of 3872 to its lowest radical form.ANSWER: 44√2
44√2 is in the lowest radical form.
Simplified Radical Form of √3872
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 √3872, we need to divide into factors.
√3872 = √2 x √2 x √2 x √2 x √2 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 3872
4 is a perfect square and divides 3872
16 is a perfect square and divides 3872
121 is a perfect square and divides 3872
484 is a perfect square and divides 3872
1936 is a perfect square and divides 3872
Step 3: Divide To Perfect Square
Divide 3872 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 3872 in its simplest form: 44√2
How do you simplify √3872
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 3872. Divide 3872 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 44√2.
Simplified Decimal Form of √3872
The square root of 3872 is approximately 62.225 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √83 | Square root of 83 is the simplest radical form. | √83 |
| √89 | Square root of 89 is the simplest radical form. | √89 |
| √81 | 9√1 | √3 x √3 x √3 x √3 |
| √721 | Square root of 721 is the simplest radical form. | √7 x √103 |
| √849 | Square root of 849 is the simplest radical form. | √3 x √283 |
| √906 | Square root of 906 is the simplest radical form. | √2 x √3 x √151 |
| √6063 | Square root of 6063 is the simplest radical form. | √3 x √43 x √47 |
| √4553 | Square root of 4553 is the simplest radical form. | √29 x √157 |
| √6716 | 2√1679 | √2 x √2 x √23 x √73 |