Square Root Of 3200 In Simplest Radical Form
Simplify the square root of 3200 to its lowest radical form.ANSWER: 40√2
40√2 is in the lowest radical form.
Simplified Radical Form of √3200
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 √3200, we need to divide into factors.
√3200 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 3200
4 is a perfect square and divides 3200
16 is a perfect square and divides 3200
25 is a perfect square and divides 3200
64 is a perfect square and divides 3200
100 is a perfect square and divides 3200
400 is a perfect square and divides 3200
1600 is a perfect square and divides 3200
Step 3: Divide To Perfect Square
Divide 3200 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 3200 in its simplest form: 40√2
How do you simplify √3200
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 3200. Divide 3200 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 40√2.
Simplified Decimal Form of √3200
The square root of 3200 is approximately 56.569 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √61 | Square root of 61 is the simplest radical form. | √61 |
| √35 | Square root of 35 is the simplest radical form. | √5 x √7 |
| √73 | Square root of 73 is the simplest radical form. | √73 |
| √880 | 4√55 | √2 x √2 x √2 x √2 x √5 x √11 |
| √805 | Square root of 805 is the simplest radical form. | √5 x √7 x √23 |
| √913 | Square root of 913 is the simplest radical form. | √11 x √83 |
| √7990 | Square root of 7990 is the simplest radical form. | √2 x √5 x √17 x √47 |
| √2082 | Square root of 2082 is the simplest radical form. | √2 x √3 x √347 |
| √3570 | Square root of 3570 is the simplest radical form. | √2 x √3 x √5 x √7 x √17 |