Square Root Of 43046721 In Simplest Radical Form
Simplify the square root of 43046721 to its lowest radical form.ANSWER: 6561√1
6561√1 is in the lowest radical form.
Simplified Radical Form of √43046721
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 √43046721, we need to divide into factors.
√43046721 = √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 43046721
9 is a perfect square and divides 43046721
81 is a perfect square and divides 43046721
729 is a perfect square and divides 43046721
6561 is a perfect square and divides 43046721
59049 is a perfect square and divides 43046721
531441 is a perfect square and divides 43046721
4782969 is a perfect square and divides 43046721
43046721 is a perfect square and divides 43046721
Step 3: Divide To Perfect Square
Divide 43046721 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 43046721 in its simplest form: 6561√1
How do you simplify √43046721
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 43046721. Divide 43046721 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 6561√1.
Simplified Decimal Form of √43046721
The square root of 43046721 is approximately 6561 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √21 | Square root of 21 is the simplest radical form. | √3 x √7 |
| √23 | Square root of 23 is the simplest radical form. | √23 |
| √78 | Square root of 78 is the simplest radical form. | √2 x √3 x √13 |
| √356 | 2√89 | √2 x √2 x √89 |
| √170 | Square root of 170 is the simplest radical form. | √2 x √5 x √17 |
| √503 | Square root of 503 is the simplest radical form. | √503 |
| √5513 | Square root of 5513 is the simplest radical form. | √37 x √149 |
| √8810 | Square root of 8810 is the simplest radical form. | √2 x √5 x √881 |
| √6360 | 2√1590 | √2 x √2 x √2 x √3 x √5 x √53 |