Square Root Of 216000 In Simplest Radical Form
Simplify the square root of 216000 to its lowest radical form.ANSWER: 120√15
120√15 is in the lowest radical form.
Simplified Radical Form of √216000
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 √216000, we need to divide into factors.
√216000 = √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √5 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 216000
4 is a perfect square and divides 216000
9 is a perfect square and divides 216000
16 is a perfect square and divides 216000
25 is a perfect square and divides 216000
36 is a perfect square and divides 216000
64 is a perfect square and divides 216000
100 is a perfect square and divides 216000
144 is a perfect square and divides 216000
225 is a perfect square and divides 216000
400 is a perfect square and divides 216000
576 is a perfect square and divides 216000
900 is a perfect square and divides 216000
1600 is a perfect square and divides 216000
3600 is a perfect square and divides 216000
14400 is a perfect square and divides 216000
Step 3: Divide To Perfect Square
Divide 216000 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 216000 in its simplest form: 120√15
How do you simplify √216000
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 216000. Divide 216000 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 120√15.
Simplified Decimal Form of √216000
The square root of 216000 is approximately 464.758 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √38 | Square root of 38 is the simplest radical form. | √2 x √19 |
| √59 | Square root of 59 is the simplest radical form. | √59 |
| √81 | 9√1 | √3 x √3 x √3 x √3 |
| √400 | 20√1 | √2 x √2 x √2 x √2 x √5 x √5 |
| √457 | Square root of 457 is the simplest radical form. | √457 |
| √909 | 3√101 | √3 x √3 x √101 |
| √2654 | Square root of 2654 is the simplest radical form. | √2 x √1327 |
| √8103 | Square root of 8103 is the simplest radical form. | √3 x √37 x √73 |
| √2003 | Square root of 2003 is the simplest radical form. | √2003 |