Square Root Of 2007 In Simplest Radical Form
Simplify the square root of 2007 to its lowest radical form.ANSWER: 3√223
3√223 is in the lowest radical form.
Simplified Radical Form of √2007
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 √2007, we need to divide into factors.
√2007 = √3 x √3 x √223Step 2: List Perfect Squares
1 is a perfect square and divides 2007
9 is a perfect square and divides 2007
Step 3: Divide To Perfect Square
Divide 2007 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 2007 in its simplest form: 3√223
How do you simplify √2007
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 2007. Divide 2007 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 3√223.
Simplified Decimal Form of √2007
The square root of 2007 is approximately 44.8 when expressed in decimal form.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√92 | 2√23 | √2 x √2 x √23 |
√27 | 3√3 | √3 x √3 x √3 |
√81 | 9√1 | √3 x √3 x √3 x √3 |
√935 | Square root of 935 is the simplest radical form. | √5 x √11 x √17 |
√737 | Square root of 737 is the simplest radical form. | √11 x √67 |
√786 | Square root of 786 is the simplest radical form. | √2 x √3 x √131 |
√3798 | 3√422 | √2 x √3 x √3 x √211 |
√9480 | 2√2370 | √2 x √2 x √2 x √3 x √5 x √79 |
√6911 | Square root of 6911 is the simplest radical form. | √6911 |