Square Root Of 421875 In Simplest Radical Form
Simplify the square root of 421875 to its lowest radical form.ANSWER: 375√3
375√3 is in the lowest radical form.
Simplified Radical Form of √421875
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 √421875, we need to divide into factors.
√421875 = √3 x √3 x √3 x √5 x √5 x √5 x √5 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 421875
9 is a perfect square and divides 421875
25 is a perfect square and divides 421875
225 is a perfect square and divides 421875
625 is a perfect square and divides 421875
5625 is a perfect square and divides 421875
15625 is a perfect square and divides 421875
140625 is a perfect square and divides 421875
Step 3: Divide To Perfect Square
Divide 421875 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 421875 in its simplest form: 375√3
How do you simplify √421875
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 421875. Divide 421875 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 375√3.
Simplified Decimal Form of √421875
The square root of 421875 is approximately 649.519 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √36 | 6√1 | √2 x √2 x √3 x √3 |
| √45 | 3√5 | √3 x √3 x √5 |
| √10 | Square root of 10 is the simplest radical form. | √2 x √5 |
| √876 | 2√219 | √2 x √2 x √3 x √73 |
| √443 | Square root of 443 is the simplest radical form. | √443 |
| √644 | 2√161 | √2 x √2 x √7 x √23 |
| √9645 | Square root of 9645 is the simplest radical form. | √3 x √5 x √643 |
| √7175 | 5√287 | √5 x √5 x √7 x √41 |
| √8057 | Square root of 8057 is the simplest radical form. | √7 x √1151 |