Square Root Of 57289761 In Simplest Radical Form
Simplify the square root of 57289761 to its lowest radical form.ANSWER: 7569√1
7569√1 is in the lowest radical form.
Simplified Radical Form of √57289761
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 √57289761, we need to divide into factors.
√57289761 = √3 x √3 x √3 x √3 x √29 x √29 x √29 x √29Step 2: List Perfect Squares
1 is a perfect square and divides 57289761
9 is a perfect square and divides 57289761
81 is a perfect square and divides 57289761
841 is a perfect square and divides 57289761
7569 is a perfect square and divides 57289761
68121 is a perfect square and divides 57289761
707281 is a perfect square and divides 57289761
6365529 is a perfect square and divides 57289761
57289761 is a perfect square and divides 57289761
Step 3: Divide To Perfect Square
Divide 57289761 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 57289761 in its simplest form: 7569√1
How do you simplify √57289761
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 57289761. Divide 57289761 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 7569√1.
Simplified Decimal Form of √57289761
The square root of 57289761 is approximately 7569 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √45 | 3√5 | √3 x √3 x √5 |
| √59 | Square root of 59 is the simplest radical form. | √59 |
| √57 | Square root of 57 is the simplest radical form. | √3 x √19 |
| √670 | Square root of 670 is the simplest radical form. | √2 x √5 x √67 |
| √112 | 4√7 | √2 x √2 x √2 x √2 x √7 |
| √428 | 2√107 | √2 x √2 x √107 |
| √5442 | Square root of 5442 is the simplest radical form. | √2 x √3 x √907 |
| √8594 | Square root of 8594 is the simplest radical form. | √2 x √4297 |
| √4221 | 3√469 | √3 x √3 x √7 x √67 |