Square Root Of 7200 In Simplest Radical Form
Simplify the square root of 7200 to its lowest radical form.ANSWER: 60√2
60√2 is in the lowest radical form.
Simplified Radical Form of √7200
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 √7200, we need to divide into factors.
√7200 = √2 x √2 x √2 x √2 x √2 x √3 x √3 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 7200
4 is a perfect square and divides 7200
9 is a perfect square and divides 7200
16 is a perfect square and divides 7200
25 is a perfect square and divides 7200
36 is a perfect square and divides 7200
100 is a perfect square and divides 7200
144 is a perfect square and divides 7200
225 is a perfect square and divides 7200
400 is a perfect square and divides 7200
900 is a perfect square and divides 7200
3600 is a perfect square and divides 7200
Step 3: Divide To Perfect Square
Divide 7200 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 7200 in its simplest form: 60√2
How do you simplify √7200
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 7200. Divide 7200 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 60√2.
Simplified Decimal Form of √7200
The square root of 7200 is approximately 84.853 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √8 | 2√2 | √2 x √2 x √2 |
| √6 | Square root of 6 is the simplest radical form. | √2 x √3 |
| √37 | Square root of 37 is the simplest radical form. | √37 |
| √485 | Square root of 485 is the simplest radical form. | √5 x √97 |
| √406 | Square root of 406 is the simplest radical form. | √2 x √7 x √29 |
| √794 | Square root of 794 is the simplest radical form. | √2 x √397 |
| √5535 | 3√615 | √3 x √3 x √3 x √5 x √41 |
| √7405 | Square root of 7405 is the simplest radical form. | √5 x √1481 |
| √5906 | Square root of 5906 is the simplest radical form. | √2 x √2953 |