Square Root Of 941192 In Simplest Radical Form
Simplify the square root of 941192 to its lowest radical form.ANSWER: 686√2
686√2 is in the lowest radical form.
Simplified Radical Form of √941192
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 √941192, we need to divide into factors.
√941192 = √2 x √2 x √2 x √7 x √7 x √7 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 941192
4 is a perfect square and divides 941192
49 is a perfect square and divides 941192
196 is a perfect square and divides 941192
2401 is a perfect square and divides 941192
9604 is a perfect square and divides 941192
117649 is a perfect square and divides 941192
470596 is a perfect square and divides 941192
Step 3: Divide To Perfect Square
Divide 941192 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 941192 in its simplest form: 686√2
How do you simplify √941192
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 941192. Divide 941192 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 686√2.
Simplified Decimal Form of √941192
The square root of 941192 is approximately 970.151 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √53 | Square root of 53 is the simplest radical form. | √53 |
| √13 | Square root of 13 is the simplest radical form. | √13 |
| √94 | Square root of 94 is the simplest radical form. | √2 x √47 |
| √914 | Square root of 914 is the simplest radical form. | √2 x √457 |
| √363 | 11√3 | √3 x √11 x √11 |
| √330 | Square root of 330 is the simplest radical form. | √2 x √3 x √5 x √11 |
| √4724 | 2√1181 | √2 x √2 x √1181 |
| √7327 | Square root of 7327 is the simplest radical form. | √17 x √431 |
| √7176 | 2√1794 | √2 x √2 x √2 x √3 x √13 x √23 |