Square Root Of 194481 In Simplest Radical Form
Simplify the square root of 194481 to its lowest radical form.ANSWER: 441√1
441√1 is in the lowest radical form.
Simplified Radical Form of √194481
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 √194481, we need to divide into factors.
√194481 = √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 194481
9 is a perfect square and divides 194481
49 is a perfect square and divides 194481
81 is a perfect square and divides 194481
441 is a perfect square and divides 194481
2401 is a perfect square and divides 194481
3969 is a perfect square and divides 194481
21609 is a perfect square and divides 194481
194481 is a perfect square and divides 194481
Step 3: Divide To Perfect Square
Divide 194481 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 194481 in its simplest form: 441√1
How do you simplify √194481
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 194481. Divide 194481 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 441√1.
Simplified Decimal Form of √194481
The square root of 194481 is approximately 441 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √32 | 4√2 | √2 x √2 x √2 x √2 x √2 |
| √24 | 2√6 | √2 x √2 x √2 x √3 |
| √82 | Square root of 82 is the simplest radical form. | √2 x √41 |
| √358 | Square root of 358 is the simplest radical form. | √2 x √179 |
| √225 | 15√1 | √3 x √3 x √5 x √5 |
| √126 | 3√14 | √2 x √3 x √3 x √7 |
| √2041 | Square root of 2041 is the simplest radical form. | √13 x √157 |
| √3567 | Square root of 3567 is the simplest radical form. | √3 x √29 x √41 |
| √3811 | Square root of 3811 is the simplest radical form. | √37 x √103 |