Square Root Of 857375 In Simplest Radical Form
Simplify the square root of 857375 to its lowest radical form.ANSWER: 95√95
95√95 is in the lowest radical form.
Simplified Radical Form of √857375
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 √857375, we need to divide into factors.
√857375 = √5 x √5 x √5 x √19 x √19 x √19Step 2: List Perfect Squares
1 is a perfect square and divides 857375
25 is a perfect square and divides 857375
361 is a perfect square and divides 857375
9025 is a perfect square and divides 857375
Step 3: Divide To Perfect Square
Divide 857375 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 857375 in its simplest form: 95√95
How do you simplify √857375
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 857375. Divide 857375 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 95√95.
Simplified Decimal Form of √857375
The square root of 857375 is approximately 925.945 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √60 | 2√15 | √2 x √2 x √3 x √5 |
| √25 | 5√1 | √5 x √5 |
| √38 | Square root of 38 is the simplest radical form. | √2 x √19 |
| √574 | Square root of 574 is the simplest radical form. | √2 x √7 x √41 |
| √682 | Square root of 682 is the simplest radical form. | √2 x √11 x √31 |
| √243 | 9√3 | √3 x √3 x √3 x √3 x √3 |
| √5914 | Square root of 5914 is the simplest radical form. | √2 x √2957 |
| √2927 | Square root of 2927 is the simplest radical form. | √2927 |
| √3410 | Square root of 3410 is the simplest radical form. | √2 x √5 x √11 x √31 |