Square Root Of 4100625 In Simplest Radical Form
Simplify the square root of 4100625 to its lowest radical form.ANSWER: 2025√1
2025√1 is in the lowest radical form.
Simplified Radical Form of √4100625
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 √4100625, we need to divide into factors.
√4100625 = √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √5 x √5 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 4100625
9 is a perfect square and divides 4100625
25 is a perfect square and divides 4100625
81 is a perfect square and divides 4100625
225 is a perfect square and divides 4100625
625 is a perfect square and divides 4100625
729 is a perfect square and divides 4100625
2025 is a perfect square and divides 4100625
5625 is a perfect square and divides 4100625
6561 is a perfect square and divides 4100625
18225 is a perfect square and divides 4100625
50625 is a perfect square and divides 4100625
164025 is a perfect square and divides 4100625
455625 is a perfect square and divides 4100625
4100625 is a perfect square and divides 4100625
Step 3: Divide To Perfect Square
Divide 4100625 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 4100625 in its simplest form: 2025√1
How do you simplify √4100625
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 4100625. Divide 4100625 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 2025√1.
Simplified Decimal Form of √4100625
The square root of 4100625 is approximately 2025 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √72 | 6√2 | √2 x √2 x √2 x √3 x √3 |
| √11 | Square root of 11 is the simplest radical form. | √11 |
| √21 | Square root of 21 is the simplest radical form. | √3 x √7 |
| √302 | Square root of 302 is the simplest radical form. | √2 x √151 |
| √840 | 2√210 | √2 x √2 x √2 x √3 x √5 x √7 |
| √852 | 2√213 | √2 x √2 x √3 x √71 |
| √6188 | 2√1547 | √2 x √2 x √7 x √13 x √17 |
| √9709 | Square root of 9709 is the simplest radical form. | √7 x √19 x √73 |
| √1878 | Square root of 1878 is the simplest radical form. | √2 x √3 x √313 |