Square Root Of 3748096 In Simplest Radical Form
Simplify the square root of 3748096 to its lowest radical form.ANSWER: 1936√1
1936√1 is in the lowest radical form.
Simplified Radical Form of √3748096
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 √3748096, we need to divide into factors.
√3748096 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √11 x √11 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 3748096
4 is a perfect square and divides 3748096
16 is a perfect square and divides 3748096
64 is a perfect square and divides 3748096
121 is a perfect square and divides 3748096
256 is a perfect square and divides 3748096
484 is a perfect square and divides 3748096
1936 is a perfect square and divides 3748096
7744 is a perfect square and divides 3748096
14641 is a perfect square and divides 3748096
30976 is a perfect square and divides 3748096
58564 is a perfect square and divides 3748096
234256 is a perfect square and divides 3748096
937024 is a perfect square and divides 3748096
3748096 is a perfect square and divides 3748096
Step 3: Divide To Perfect Square
Divide 3748096 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 3748096 in its simplest form: 1936√1
How do you simplify √3748096
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 3748096. Divide 3748096 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 1936√1.
Simplified Decimal Form of √3748096
The square root of 3748096 is approximately 1936 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √75 | 5√3 | √3 x √5 x √5 |
| √94 | Square root of 94 is the simplest radical form. | √2 x √47 |
| √11 | Square root of 11 is the simplest radical form. | √11 |
| √742 | Square root of 742 is the simplest radical form. | √2 x √7 x √53 |
| √907 | Square root of 907 is the simplest radical form. | √907 |
| √743 | Square root of 743 is the simplest radical form. | √743 |
| √3770 | Square root of 3770 is the simplest radical form. | √2 x √5 x √13 x √29 |
| √2436 | 2√609 | √2 x √2 x √3 x √7 x √29 |
| √5953 | Square root of 5953 is the simplest radical form. | √5953 |