Square Root Of 17850625 In Simplest Radical Form
Simplify the square root of 17850625 to its lowest radical form.ANSWER: 4225√1
4225√1 is in the lowest radical form.
Simplified Radical Form of √17850625
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 √17850625, we need to divide into factors.
√17850625 = √5 x √5 x √5 x √5 x √13 x √13 x √13 x √13Step 2: List Perfect Squares
1 is a perfect square and divides 17850625
25 is a perfect square and divides 17850625
169 is a perfect square and divides 17850625
625 is a perfect square and divides 17850625
4225 is a perfect square and divides 17850625
28561 is a perfect square and divides 17850625
105625 is a perfect square and divides 17850625
714025 is a perfect square and divides 17850625
17850625 is a perfect square and divides 17850625
Step 3: Divide To Perfect Square
Divide 17850625 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 17850625 in its simplest form: 4225√1
How do you simplify √17850625
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 17850625. Divide 17850625 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 4225√1.
Simplified Decimal Form of √17850625
The square root of 17850625 is approximately 4225 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √44 | 2√11 | √2 x √2 x √11 |
| √46 | Square root of 46 is the simplest radical form. | √2 x √23 |
| √92 | 2√23 | √2 x √2 x √23 |
| √726 | 11√6 | √2 x √3 x √11 x √11 |
| √649 | Square root of 649 is the simplest radical form. | √11 x √59 |
| √434 | Square root of 434 is the simplest radical form. | √2 x √7 x √31 |
| √6373 | Square root of 6373 is the simplest radical form. | √6373 |
| √3151 | Square root of 3151 is the simplest radical form. | √23 x √137 |
| √6077 | Square root of 6077 is the simplest radical form. | √59 x √103 |