Square Root Of 65536 In Simplest Radical Form
Simplify the square root of 65536 to its lowest radical form.ANSWER: 256√1
256√1 is in the lowest radical form.
Simplified Radical Form of √65536
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 √65536, we need to divide into factors.
√65536 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2Step 2: List Perfect Squares
1 is a perfect square and divides 65536
4 is a perfect square and divides 65536
16 is a perfect square and divides 65536
64 is a perfect square and divides 65536
256 is a perfect square and divides 65536
1024 is a perfect square and divides 65536
4096 is a perfect square and divides 65536
16384 is a perfect square and divides 65536
65536 is a perfect square and divides 65536
Step 3: Divide To Perfect Square
Divide 65536 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 65536 in its simplest form: 256√1
How do you simplify √65536
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 65536. Divide 65536 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 256√1.
Simplified Decimal Form of √65536
The square root of 65536 is approximately 256 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √16 | 4√1 | √2 x √2 x √2 x √2 |
| √78 | Square root of 78 is the simplest radical form. | √2 x √3 x √13 |
| √28 | 2√7 | √2 x √2 x √7 |
| √862 | Square root of 862 is the simplest radical form. | √2 x √431 |
| √215 | Square root of 215 is the simplest radical form. | √5 x √43 |
| √378 | 3√42 | √2 x √3 x √3 x √3 x √7 |
| √6951 | Square root of 6951 is the simplest radical form. | √3 x √7 x √331 |
| √7370 | Square root of 7370 is the simplest radical form. | √2 x √5 x √11 x √67 |
| √2195 | Square root of 2195 is the simplest radical form. | √5 x √439 |