Square Root Of 37015056 In Simplest Radical Form
Simplify the square root of 37015056 to its lowest radical form.ANSWER: 6084√1
6084√1 is in the lowest radical form.
Simplified Radical Form of √37015056
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 √37015056, we need to divide into factors.
√37015056 = √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √13 x √13 x √13 x √13Step 2: List Perfect Squares
1 is a perfect square and divides 37015056
4 is a perfect square and divides 37015056
9 is a perfect square and divides 37015056
16 is a perfect square and divides 37015056
36 is a perfect square and divides 37015056
81 is a perfect square and divides 37015056
144 is a perfect square and divides 37015056
169 is a perfect square and divides 37015056
324 is a perfect square and divides 37015056
676 is a perfect square and divides 37015056
1296 is a perfect square and divides 37015056
1521 is a perfect square and divides 37015056
2704 is a perfect square and divides 37015056
6084 is a perfect square and divides 37015056
13689 is a perfect square and divides 37015056
24336 is a perfect square and divides 37015056
28561 is a perfect square and divides 37015056
54756 is a perfect square and divides 37015056
114244 is a perfect square and divides 37015056
219024 is a perfect square and divides 37015056
257049 is a perfect square and divides 37015056
456976 is a perfect square and divides 37015056
1028196 is a perfect square and divides 37015056
2313441 is a perfect square and divides 37015056
4112784 is a perfect square and divides 37015056
9253764 is a perfect square and divides 37015056
37015056 is a perfect square and divides 37015056
Step 3: Divide To Perfect Square
Divide 37015056 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 37015056 in its simplest form: 6084√1
How do you simplify √37015056
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 37015056. Divide 37015056 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 6084√1.
Simplified Decimal Form of √37015056
The square root of 37015056 is approximately 6084 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √86 | Square root of 86 is the simplest radical form. | √2 x √43 |
| √78 | Square root of 78 is the simplest radical form. | √2 x √3 x √13 |
| √37 | Square root of 37 is the simplest radical form. | √37 |
| √309 | Square root of 309 is the simplest radical form. | √3 x √103 |
| √116 | 2√29 | √2 x √2 x √29 |
| √812 | 2√203 | √2 x √2 x √7 x √29 |
| √5537 | 7√113 | √7 x √7 x √113 |
| √5388 | 2√1347 | √2 x √2 x √3 x √449 |
| √9931 | Square root of 9931 is the simplest radical form. | √9931 |