Square Root Of 185193 In Simplest Radical Form
Simplify the square root of 185193 to its lowest radical form.ANSWER: 57√57
57√57 is in the lowest radical form.
Simplified Radical Form of √185193
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 √185193, we need to divide into factors.
√185193 = √3 x √3 x √3 x √19 x √19 x √19Step 2: List Perfect Squares
1 is a perfect square and divides 185193
9 is a perfect square and divides 185193
361 is a perfect square and divides 185193
3249 is a perfect square and divides 185193
Step 3: Divide To Perfect Square
Divide 185193 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 185193 in its simplest form: 57√57
How do you simplify √185193
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 185193. Divide 185193 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 57√57.
Simplified Decimal Form of √185193
The square root of 185193 is approximately 430.341 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √5 | Square root of 5 is the simplest radical form. | √5 |
| √48 | 4√3 | √2 x √2 x √2 x √2 x √3 |
| √90 | 3√10 | √2 x √3 x √3 x √5 |
| √846 | 3√94 | √2 x √3 x √3 x √47 |
| √544 | 4√34 | √2 x √2 x √2 x √2 x √2 x √17 |
| √813 | Square root of 813 is the simplest radical form. | √3 x √271 |
| √5559 | Square root of 5559 is the simplest radical form. | √3 x √17 x √109 |
| √9879 | Square root of 9879 is the simplest radical form. | √3 x √37 x √89 |
| √2262 | Square root of 2262 is the simplest radical form. | √2 x √3 x √13 x √29 |