Square Root Of 6848 In Simplest Radical Form
Simplify the square root of 6848 to its lowest radical form.ANSWER: 8√107
8√107 is in the lowest radical form.
Simplified Radical Form of √6848
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 √6848, we need to divide into factors.
√6848 = √2 x √2 x √2 x √2 x √2 x √2 x √107Step 2: List Perfect Squares
1 is a perfect square and divides 6848
4 is a perfect square and divides 6848
16 is a perfect square and divides 6848
64 is a perfect square and divides 6848
Step 3: Divide To Perfect Square
Divide 6848 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 6848 in its simplest form: 8√107
How do you simplify √6848
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 6848. Divide 6848 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√107.
Simplified Decimal Form of √6848
The square root of 6848 is approximately 82.753 when expressed in decimal form.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√44 | 2√11 | √2 x √2 x √11 |
√57 | Square root of 57 is the simplest radical form. | √3 x √19 |
√9 | 3√1 | √3 x √3 |
√342 | 3√38 | √2 x √3 x √3 x √19 |
√808 | 2√202 | √2 x √2 x √2 x √101 |
√852 | 2√213 | √2 x √2 x √3 x √71 |
√9729 | 3√1081 | √3 x √3 x √23 x √47 |
√1502 | Square root of 1502 is the simplest radical form. | √2 x √751 |
√3406 | Square root of 3406 is the simplest radical form. | √2 x √13 x √131 |