Square Root Of 4072 In Simplest Radical Form
Simplify the square root of 4072 to its lowest radical form.ANSWER: 2√1018
2√1018 is in the lowest radical form.
Simplified Radical Form of √4072
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 √4072, we need to divide into factors.
√4072 = √2 x √2 x √2 x √509Step 2: List Perfect Squares
1 is a perfect square and divides 4072
4 is a perfect square and divides 4072
Step 3: Divide To Perfect Square
Divide 4072 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 4072 in its simplest form: 2√1018
How do you simplify √4072
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 4072. Divide 4072 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√1018.
Simplified Decimal Form of √4072
The square root of 4072 is approximately 63.812 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √66 | Square root of 66 is the simplest radical form. | √2 x √3 x √11 |
| √35 | Square root of 35 is the simplest radical form. | √5 x √7 |
| √78 | Square root of 78 is the simplest radical form. | √2 x √3 x √13 |
| √110 | Square root of 110 is the simplest radical form. | √2 x √5 x √11 |
| √702 | 3√78 | √2 x √3 x √3 x √3 x √13 |
| √943 | Square root of 943 is the simplest radical form. | √23 x √41 |
| √5397 | Square root of 5397 is the simplest radical form. | √3 x √7 x √257 |
| √5253 | Square root of 5253 is the simplest radical form. | √3 x √17 x √103 |
| √8781 | Square root of 8781 is the simplest radical form. | √3 x √2927 |