Square Root Of 10556001 In Simplest Radical Form
Simplify the square root of 10556001 to its lowest radical form.ANSWER: 3249√1
3249√1 is in the lowest radical form.
Simplified Radical Form of √10556001
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 √10556001, we need to divide into factors.
√10556001 = √3 x √3 x √3 x √3 x √19 x √19 x √19 x √19Step 2: List Perfect Squares
1 is a perfect square and divides 10556001
9 is a perfect square and divides 10556001
81 is a perfect square and divides 10556001
361 is a perfect square and divides 10556001
3249 is a perfect square and divides 10556001
29241 is a perfect square and divides 10556001
130321 is a perfect square and divides 10556001
1172889 is a perfect square and divides 10556001
10556001 is a perfect square and divides 10556001
Step 3: Divide To Perfect Square
Divide 10556001 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 10556001 in its simplest form: 3249√1
How do you simplify √10556001
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 10556001. Divide 10556001 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 3249√1.
Simplified Decimal Form of √10556001
The square root of 10556001 is approximately 3249 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √19 | Square root of 19 is the simplest radical form. | √19 |
| √76 | 2√19 | √2 x √2 x √19 |
| √12 | 2√3 | √2 x √2 x √3 |
| √272 | 4√17 | √2 x √2 x √2 x √2 x √17 |
| √906 | Square root of 906 is the simplest radical form. | √2 x √3 x √151 |
| √755 | Square root of 755 is the simplest radical form. | √5 x √151 |
| √1775 | 5√71 | √5 x √5 x √71 |
| √8727 | Square root of 8727 is the simplest radical form. | √3 x √2909 |
| √5758 | Square root of 5758 is the simplest radical form. | √2 x √2879 |