Square Root Of 22667121 In Simplest Radical Form
Simplify the square root of 22667121 to its lowest radical form.ANSWER: 4761√1
4761√1 is in the lowest radical form.
Simplified Radical Form of √22667121
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 √22667121, we need to divide into factors.
√22667121 = √3 x √3 x √3 x √3 x √23 x √23 x √23 x √23Step 2: List Perfect Squares
1 is a perfect square and divides 22667121
9 is a perfect square and divides 22667121
81 is a perfect square and divides 22667121
529 is a perfect square and divides 22667121
4761 is a perfect square and divides 22667121
42849 is a perfect square and divides 22667121
279841 is a perfect square and divides 22667121
2518569 is a perfect square and divides 22667121
22667121 is a perfect square and divides 22667121
Step 3: Divide To Perfect Square
Divide 22667121 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 22667121 in its simplest form: 4761√1
How do you simplify √22667121
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 22667121. Divide 22667121 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 4761√1.
Simplified Decimal Form of √22667121
The square root of 22667121 is approximately 4761 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √84 | 2√21 | √2 x √2 x √3 x √7 |
| √7 | Square root of 7 is the simplest radical form. | √7 |
| √85 | Square root of 85 is the simplest radical form. | √5 x √17 |
| √229 | Square root of 229 is the simplest radical form. | √229 |
| √799 | Square root of 799 is the simplest radical form. | √17 x √47 |
| √725 | 5√29 | √5 x √5 x √29 |
| √6552 | 6√182 | √2 x √2 x √2 x √3 x √3 x √7 x √13 |
| √5558 | Square root of 5558 is the simplest radical form. | √2 x √7 x √397 |
| √5965 | Square root of 5965 is the simplest radical form. | √5 x √1193 |