Square Root Of 3112 In Simplest Radical Form
Simplify the square root of 3112 to its lowest radical form.ANSWER: 2√778
2√778 is in the lowest radical form.
Simplified Radical Form of √3112
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 √3112, we need to divide into factors.
√3112 = √2 x √2 x √2 x √389Step 2: List Perfect Squares
1 is a perfect square and divides 3112
4 is a perfect square and divides 3112
Step 3: Divide To Perfect Square
Divide 3112 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 3112 in its simplest form: 2√778
How do you simplify √3112
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 3112. Divide 3112 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√778.
Simplified Decimal Form of √3112
The square root of 3112 is approximately 55.785 when expressed in decimal form.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√35 | Square root of 35 is the simplest radical form. | √5 x √7 |
√76 | 2√19 | √2 x √2 x √19 |
√40 | 2√10 | √2 x √2 x √2 x √5 |
√319 | Square root of 319 is the simplest radical form. | √11 x √29 |
√173 | Square root of 173 is the simplest radical form. | √173 |
√845 | 13√5 | √5 x √13 x √13 |
√6874 | Square root of 6874 is the simplest radical form. | √2 x √7 x √491 |
√2858 | Square root of 2858 is the simplest radical form. | √2 x √1429 |
√1316 | 2√329 | √2 x √2 x √7 x √47 |