Square Root Of 15752961 In Simplest Radical Form
Simplify the square root of 15752961 to its lowest radical form.ANSWER: 3969√1
3969√1 is in the lowest radical form.
Simplified Radical Form of √15752961
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 √15752961, we need to divide into factors.
√15752961 = √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √7 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 15752961
9 is a perfect square and divides 15752961
49 is a perfect square and divides 15752961
81 is a perfect square and divides 15752961
441 is a perfect square and divides 15752961
729 is a perfect square and divides 15752961
2401 is a perfect square and divides 15752961
3969 is a perfect square and divides 15752961
6561 is a perfect square and divides 15752961
21609 is a perfect square and divides 15752961
35721 is a perfect square and divides 15752961
194481 is a perfect square and divides 15752961
321489 is a perfect square and divides 15752961
1750329 is a perfect square and divides 15752961
15752961 is a perfect square and divides 15752961
Step 3: Divide To Perfect Square
Divide 15752961 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 15752961 in its simplest form: 3969√1
How do you simplify √15752961
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 15752961. Divide 15752961 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 3969√1.
Simplified Decimal Form of √15752961
The square root of 15752961 is approximately 3969 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √67 | Square root of 67 is the simplest radical form. | √67 |
| √99 | 3√11 | √3 x √3 x √11 |
| √85 | Square root of 85 is the simplest radical form. | √5 x √17 |
| √532 | 2√133 | √2 x √2 x √7 x √19 |
| √121 | 11√1 | √11 x √11 |
| √305 | Square root of 305 is the simplest radical form. | √5 x √61 |
| √9352 | 2√2338 | √2 x √2 x √2 x √7 x √167 |
| √7596 | 6√211 | √2 x √2 x √3 x √3 x √211 |
| √8448 | 16√33 | √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √11 |