Square Root Of 6784 In Simplest Radical Form
Simplify the square root of 6784 to its lowest radical form.ANSWER: 8√106
8√106 is in the lowest radical form.
Simplified Radical Form of √6784
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 √6784, we need to divide into factors.
√6784 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √53Step 2: List Perfect Squares
1 is a perfect square and divides 6784
4 is a perfect square and divides 6784
16 is a perfect square and divides 6784
64 is a perfect square and divides 6784
Step 3: Divide To Perfect Square
Divide 6784 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 6784 in its simplest form: 8√106
How do you simplify √6784
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 6784. Divide 6784 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 8√106.
Simplified Decimal Form of √6784
The square root of 6784 is approximately 82.365 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √95 | Square root of 95 is the simplest radical form. | √5 x √19 |
| √19 | Square root of 19 is the simplest radical form. | √19 |
| √58 | Square root of 58 is the simplest radical form. | √2 x √29 |
| √120 | 2√30 | √2 x √2 x √2 x √3 x √5 |
| √802 | Square root of 802 is the simplest radical form. | √2 x √401 |
| √218 | Square root of 218 is the simplest radical form. | √2 x √109 |
| √7370 | Square root of 7370 is the simplest radical form. | √2 x √5 x √11 x √67 |
| √2762 | Square root of 2762 is the simplest radical form. | √2 x √1381 |
| √3003 | Square root of 3003 is the simplest radical form. | √3 x √7 x √11 x √13 |