Square Root Of 6912 In Simplest Radical Form
Simplify the square root of 6912 to its lowest radical form.ANSWER: 48√3
48√3 is in the lowest radical form.
Simplified Radical Form of √6912
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 √6912, we need to divide into factors.
√6912 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 6912
4 is a perfect square and divides 6912
9 is a perfect square and divides 6912
16 is a perfect square and divides 6912
36 is a perfect square and divides 6912
64 is a perfect square and divides 6912
144 is a perfect square and divides 6912
256 is a perfect square and divides 6912
576 is a perfect square and divides 6912
2304 is a perfect square and divides 6912
Step 3: Divide To Perfect Square
Divide 6912 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 6912 in its simplest form: 48√3
How do you simplify √6912
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 6912. Divide 6912 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 48√3.
Simplified Decimal Form of √6912
The square root of 6912 is approximately 83.138 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √32 | 4√2 | √2 x √2 x √2 x √2 x √2 |
| √28 | 2√7 | √2 x √2 x √7 |
| √72 | 6√2 | √2 x √2 x √2 x √3 x √3 |
| √669 | Square root of 669 is the simplest radical form. | √3 x √223 |
| √352 | 4√22 | √2 x √2 x √2 x √2 x √2 x √11 |
| √798 | Square root of 798 is the simplest radical form. | √2 x √3 x √7 x √19 |
| √6862 | Square root of 6862 is the simplest radical form. | √2 x √47 x √73 |
| √5919 | Square root of 5919 is the simplest radical form. | √3 x √1973 |
| √9020 | 2√2255 | √2 x √2 x √5 x √11 x √41 |