Square Root Of 6250000 In Simplest Radical Form
Simplify the square root of 6250000 to its lowest radical form.ANSWER: 2500√1
2500√1 is in the lowest radical form.
Simplified Radical Form of √6250000
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 √6250000, we need to divide into factors.
√6250000 = √2 x √2 x √2 x √2 x √5 x √5 x √5 x √5 x √5 x √5 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 6250000
4 is a perfect square and divides 6250000
16 is a perfect square and divides 6250000
25 is a perfect square and divides 6250000
100 is a perfect square and divides 6250000
400 is a perfect square and divides 6250000
625 is a perfect square and divides 6250000
2500 is a perfect square and divides 6250000
10000 is a perfect square and divides 6250000
15625 is a perfect square and divides 6250000
62500 is a perfect square and divides 6250000
250000 is a perfect square and divides 6250000
390625 is a perfect square and divides 6250000
1562500 is a perfect square and divides 6250000
6250000 is a perfect square and divides 6250000
Step 3: Divide To Perfect Square
Divide 6250000 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 6250000 in its simplest form: 2500√1
How do you simplify √6250000
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 6250000. Divide 6250000 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 2500√1.
Simplified Decimal Form of √6250000
The square root of 6250000 is approximately 2500 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √68 | 2√17 | √2 x √2 x √17 |
| √9 | 3√1 | √3 x √3 |
| √29 | Square root of 29 is the simplest radical form. | √29 |
| √540 | 6√15 | √2 x √2 x √3 x √3 x √3 x √5 |
| √104 | 2√26 | √2 x √2 x √2 x √13 |
| √727 | Square root of 727 is the simplest radical form. | √727 |
| √8910 | 9√110 | √2 x √3 x √3 x √3 x √3 x √5 x √11 |
| √4578 | Square root of 4578 is the simplest radical form. | √2 x √3 x √7 x √109 |
| √9193 | Square root of 9193 is the simplest radical form. | √29 x √317 |