Square Root Of 32768 In Simplest Radical Form
Simplify the square root of 32768 to its lowest radical form.ANSWER: 128√2
128√2 is in the lowest radical form.
Simplified Radical Form of √32768
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 √32768, we need to divide into factors.
√32768 = √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 32768
4 is a perfect square and divides 32768
16 is a perfect square and divides 32768
64 is a perfect square and divides 32768
256 is a perfect square and divides 32768
1024 is a perfect square and divides 32768
4096 is a perfect square and divides 32768
16384 is a perfect square and divides 32768
Step 3: Divide To Perfect Square
Divide 32768 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 32768 in its simplest form: 128√2
How do you simplify √32768
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 32768. Divide 32768 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 128√2.
Simplified Decimal Form of √32768
The square root of 32768 is approximately 181.019 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √20 | 2√5 | √2 x √2 x √5 |
| √59 | Square root of 59 is the simplest radical form. | √59 |
| √18 | 3√2 | √2 x √3 x √3 |
| √944 | 4√59 | √2 x √2 x √2 x √2 x √59 |
| √252 | 6√7 | √2 x √2 x √3 x √3 x √7 |
| √254 | Square root of 254 is the simplest radical form. | √2 x √127 |
| √5122 | Square root of 5122 is the simplest radical form. | √2 x √13 x √197 |
| √9797 | Square root of 9797 is the simplest radical form. | √97 x √101 |
| √1228 | 2√307 | √2 x √2 x √307 |