Square Root Of 681472 In Simplest Radical Form
Simplify the square root of 681472 to its lowest radical form.ANSWER: 176√22
176√22 is in the lowest radical form.
Simplified Radical Form of √681472
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 √681472, we need to divide into factors.
√681472 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √11 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 681472
4 is a perfect square and divides 681472
16 is a perfect square and divides 681472
64 is a perfect square and divides 681472
121 is a perfect square and divides 681472
256 is a perfect square and divides 681472
484 is a perfect square and divides 681472
1936 is a perfect square and divides 681472
7744 is a perfect square and divides 681472
30976 is a perfect square and divides 681472
Step 3: Divide To Perfect Square
Divide 681472 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 681472 in its simplest form: 176√22
How do you simplify √681472
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 681472. Divide 681472 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 176√22.
Simplified Decimal Form of √681472
The square root of 681472 is approximately 825.513 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √38 | Square root of 38 is the simplest radical form. | √2 x √19 |
| √48 | 4√3 | √2 x √2 x √2 x √2 x √3 |
| √82 | Square root of 82 is the simplest radical form. | √2 x √41 |
| √401 | Square root of 401 is the simplest radical form. | √401 |
| √407 | Square root of 407 is the simplest radical form. | √11 x √37 |
| √139 | Square root of 139 is the simplest radical form. | √139 |
| √4790 | Square root of 4790 is the simplest radical form. | √2 x √5 x √479 |
| √5022 | 9√62 | √2 x √3 x √3 x √3 x √3 x √31 |
| √2258 | Square root of 2258 is the simplest radical form. | √2 x √1129 |