Square Root Of 6868 In Simplest Radical Form
Simplify the square root of 6868 to its lowest radical form.ANSWER: 2√1717
2√1717 is in the lowest radical form.
Simplified Radical Form of √6868
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 √6868, we need to divide into factors.
√6868 = √2 x √2 x √17 x √101Step 2: List Perfect Squares
1 is a perfect square and divides 6868
4 is a perfect square and divides 6868
Step 3: Divide To Perfect Square
Divide 6868 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 6868 in its simplest form: 2√1717
How do you simplify √6868
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 6868. Divide 6868 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 2√1717.
Simplified Decimal Form of √6868
The square root of 6868 is approximately 82.873 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √19 | Square root of 19 is the simplest radical form. | √19 |
| √65 | Square root of 65 is the simplest radical form. | √5 x √13 |
| √26 | Square root of 26 is the simplest radical form. | √2 x √13 |
| √318 | Square root of 318 is the simplest radical form. | √2 x √3 x √53 |
| √671 | Square root of 671 is the simplest radical form. | √11 x √61 |
| √663 | Square root of 663 is the simplest radical form. | √3 x √13 x √17 |
| √8054 | Square root of 8054 is the simplest radical form. | √2 x √4027 |
| √6202 | Square root of 6202 is the simplest radical form. | √2 x √7 x √443 |
| √3441 | Square root of 3441 is the simplest radical form. | √3 x √31 x √37 |