Square Root Of 125000 In Simplest Radical Form
Simplify the square root of 125000 to its lowest radical form.ANSWER: 250√2
250√2 is in the lowest radical form.
Simplified Radical Form of √125000
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 √125000, we need to divide into factors.
√125000 = √2 x √2 x √2 x √5 x √5 x √5 x √5 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 125000
4 is a perfect square and divides 125000
25 is a perfect square and divides 125000
100 is a perfect square and divides 125000
625 is a perfect square and divides 125000
2500 is a perfect square and divides 125000
15625 is a perfect square and divides 125000
62500 is a perfect square and divides 125000
Step 3: Divide To Perfect Square
Divide 125000 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 125000 in its simplest form: 250√2
How do you simplify √125000
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 125000. Divide 125000 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 250√2.
Simplified Decimal Form of √125000
The square root of 125000 is approximately 353.553 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √28 | 2√7 | √2 x √2 x √7 |
| √47 | Square root of 47 is the simplest radical form. | √47 |
| √17 | Square root of 17 is the simplest radical form. | √17 |
| √516 | 2√129 | √2 x √2 x √3 x √43 |
| √208 | 4√13 | √2 x √2 x √2 x √2 x √13 |
| √995 | Square root of 995 is the simplest radical form. | √5 x √199 |
| √4504 | 2√1126 | √2 x √2 x √2 x √563 |
| √7875 | 15√35 | √3 x √3 x √5 x √5 x √5 x √7 |
| √8134 | 7√166 | √2 x √7 x √7 x √83 |