Square Root Of 729000 In Simplest Radical Form
Simplify the square root of 729000 to its lowest radical form.ANSWER: 270√10
270√10 is in the lowest radical form.
Simplified Radical Form of √729000
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 √729000, we need to divide into factors.
√729000 = √2 x √2 x √2 x √3 x √3 x √3 x √3 x √3 x √3 x √5 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 729000
4 is a perfect square and divides 729000
9 is a perfect square and divides 729000
25 is a perfect square and divides 729000
36 is a perfect square and divides 729000
81 is a perfect square and divides 729000
100 is a perfect square and divides 729000
225 is a perfect square and divides 729000
324 is a perfect square and divides 729000
729 is a perfect square and divides 729000
900 is a perfect square and divides 729000
2025 is a perfect square and divides 729000
2916 is a perfect square and divides 729000
8100 is a perfect square and divides 729000
18225 is a perfect square and divides 729000
72900 is a perfect square and divides 729000
Step 3: Divide To Perfect Square
Divide 729000 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 729000 in its simplest form: 270√10
How do you simplify √729000
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 729000. Divide 729000 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 270√10.
Simplified Decimal Form of √729000
The square root of 729000 is approximately 853.815 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √20 | 2√5 | √2 x √2 x √5 |
| √77 | Square root of 77 is the simplest radical form. | √7 x √11 |
| √9 | 3√1 | √3 x √3 |
| √319 | Square root of 319 is the simplest radical form. | √11 x √29 |
| √624 | 4√39 | √2 x √2 x √2 x √2 x √3 x √13 |
| √691 | Square root of 691 is the simplest radical form. | √691 |
| √4123 | Square root of 4123 is the simplest radical form. | √7 x √19 x √31 |
| √8196 | 2√2049 | √2 x √2 x √3 x √683 |
| √7444 | 2√1861 | √2 x √2 x √1861 |