Square Root Of 3111696 In Simplest Radical Form
Simplify the square root of 3111696 to its lowest radical form.ANSWER: 1764√1
1764√1 is in the lowest radical form.
Simplified Radical Form of √3111696
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 √3111696, we need to divide into factors.
√3111696 = √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √7 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 3111696
4 is a perfect square and divides 3111696
9 is a perfect square and divides 3111696
16 is a perfect square and divides 3111696
36 is a perfect square and divides 3111696
49 is a perfect square and divides 3111696
81 is a perfect square and divides 3111696
144 is a perfect square and divides 3111696
196 is a perfect square and divides 3111696
324 is a perfect square and divides 3111696
441 is a perfect square and divides 3111696
784 is a perfect square and divides 3111696
1296 is a perfect square and divides 3111696
1764 is a perfect square and divides 3111696
2401 is a perfect square and divides 3111696
3969 is a perfect square and divides 3111696
7056 is a perfect square and divides 3111696
9604 is a perfect square and divides 3111696
15876 is a perfect square and divides 3111696
21609 is a perfect square and divides 3111696
38416 is a perfect square and divides 3111696
63504 is a perfect square and divides 3111696
86436 is a perfect square and divides 3111696
194481 is a perfect square and divides 3111696
345744 is a perfect square and divides 3111696
777924 is a perfect square and divides 3111696
3111696 is a perfect square and divides 3111696
Step 3: Divide To Perfect Square
Divide 3111696 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 3111696 in its simplest form: 1764√1
How do you simplify √3111696
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 3111696. Divide 3111696 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 1764√1.
Simplified Decimal Form of √3111696
The square root of 3111696 is approximately 1764 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √13 | Square root of 13 is the simplest radical form. | √13 |
| √54 | 3√6 | √2 x √3 x √3 x √3 |
| √40 | 2√10 | √2 x √2 x √2 x √5 |
| √384 | 8√6 | √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 |
| √786 | Square root of 786 is the simplest radical form. | √2 x √3 x √131 |
| √431 | Square root of 431 is the simplest radical form. | √431 |
| √1678 | Square root of 1678 is the simplest radical form. | √2 x √839 |
| √6506 | Square root of 6506 is the simplest radical form. | √2 x √3253 |
| √4108 | 2√1027 | √2 x √2 x √13 x √79 |