Square Root Of 512000 In Simplest Radical Form
Simplify the square root of 512000 to its lowest radical form.ANSWER: 320√5
320√5 is in the lowest radical form.
Simplified Radical Form of √512000
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 √512000, we need to divide into factors.
√512000 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √5 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 512000
4 is a perfect square and divides 512000
16 is a perfect square and divides 512000
25 is a perfect square and divides 512000
64 is a perfect square and divides 512000
100 is a perfect square and divides 512000
256 is a perfect square and divides 512000
400 is a perfect square and divides 512000
1024 is a perfect square and divides 512000
1600 is a perfect square and divides 512000
4096 is a perfect square and divides 512000
6400 is a perfect square and divides 512000
25600 is a perfect square and divides 512000
102400 is a perfect square and divides 512000
Step 3: Divide To Perfect Square
Divide 512000 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 512000 in its simplest form: 320√5
How do you simplify √512000
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 512000. Divide 512000 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 320√5.
Simplified Decimal Form of √512000
The square root of 512000 is approximately 715.542 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √84 | 2√21 | √2 x √2 x √3 x √7 |
| √58 | Square root of 58 is the simplest radical form. | √2 x √29 |
| √56 | 2√14 | √2 x √2 x √2 x √7 |
| √822 | Square root of 822 is the simplest radical form. | √2 x √3 x √137 |
| √512 | 16√2 | √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 |
| √779 | Square root of 779 is the simplest radical form. | √19 x √41 |
| √1843 | Square root of 1843 is the simplest radical form. | √19 x √97 |
| √2789 | Square root of 2789 is the simplest radical form. | √2789 |
| √1122 | Square root of 1122 is the simplest radical form. | √2 x √3 x √11 x √17 |