Square Root Of 592704 In Simplest Radical Form
Simplify the square root of 592704 to its lowest radical form.ANSWER: 168√21
168√21 is in the lowest radical form.
Simplified Radical Form of √592704
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 √592704, we need to divide into factors.
√592704 = √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 592704
4 is a perfect square and divides 592704
9 is a perfect square and divides 592704
16 is a perfect square and divides 592704
36 is a perfect square and divides 592704
49 is a perfect square and divides 592704
64 is a perfect square and divides 592704
144 is a perfect square and divides 592704
196 is a perfect square and divides 592704
441 is a perfect square and divides 592704
576 is a perfect square and divides 592704
784 is a perfect square and divides 592704
1764 is a perfect square and divides 592704
3136 is a perfect square and divides 592704
7056 is a perfect square and divides 592704
28224 is a perfect square and divides 592704
Step 3: Divide To Perfect Square
Divide 592704 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 592704 in its simplest form: 168√21
How do you simplify √592704
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 592704. Divide 592704 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 168√21.
Simplified Decimal Form of √592704
The square root of 592704 is approximately 769.873 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √78 | Square root of 78 is the simplest radical form. | √2 x √3 x √13 |
| √69 | Square root of 69 is the simplest radical form. | √3 x √23 |
| √50 | 5√2 | √2 x √5 x √5 |
| √498 | Square root of 498 is the simplest radical form. | √2 x √3 x √83 |
| √204 | 2√51 | √2 x √2 x √3 x √17 |
| √325 | 5√13 | √5 x √5 x √13 |
| √3486 | Square root of 3486 is the simplest radical form. | √2 x √3 x √7 x √83 |
| √5837 | Square root of 5837 is the simplest radical form. | √13 x √449 |
| √6920 | 2√1730 | √2 x √2 x √2 x √5 x √173 |