Square Root Of 6400 In Simplest Radical Form
Simplify the square root of 6400 to its lowest radical form.ANSWER: 80√1
80√1 is in the lowest radical form.
Simplified Radical Form of √6400
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 √6400, we need to divide into factors.
√6400 = √2 x √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 6400
4 is a perfect square and divides 6400
16 is a perfect square and divides 6400
25 is a perfect square and divides 6400
64 is a perfect square and divides 6400
100 is a perfect square and divides 6400
256 is a perfect square and divides 6400
400 is a perfect square and divides 6400
1600 is a perfect square and divides 6400
6400 is a perfect square and divides 6400
Step 3: Divide To Perfect Square
Divide 6400 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 6400 in its simplest form: 80√1
How do you simplify √6400
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 6400. Divide 6400 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 80√1.
Simplified Decimal Form of √6400
The square root of 6400 is approximately 80 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √36 | 6√1 | √2 x √2 x √3 x √3 |
| √6 | Square root of 6 is the simplest radical form. | √2 x √3 |
| √80 | 4√5 | √2 x √2 x √2 x √2 x √5 |
| √430 | Square root of 430 is the simplest radical form. | √2 x √5 x √43 |
| √192 | 8√3 | √2 x √2 x √2 x √2 x √2 x √2 x √3 |
| √470 | Square root of 470 is the simplest radical form. | √2 x √5 x √47 |
| √6822 | 3√758 | √2 x √3 x √3 x √379 |
| √5833 | Square root of 5833 is the simplest radical form. | √19 x √307 |
| √5280 | 4√330 | √2 x √2 x √2 x √2 x √2 x √3 x √5 x √11 |