Square Root Of 20736 In Simplest Radical Form
Simplify the square root of 20736 to its lowest radical form.ANSWER: 144√1
144√1 is in the lowest radical form.
Simplified Radical Form of √20736
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 √20736, we need to divide into factors.
√20736 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 20736
4 is a perfect square and divides 20736
9 is a perfect square and divides 20736
16 is a perfect square and divides 20736
36 is a perfect square and divides 20736
64 is a perfect square and divides 20736
81 is a perfect square and divides 20736
144 is a perfect square and divides 20736
256 is a perfect square and divides 20736
324 is a perfect square and divides 20736
576 is a perfect square and divides 20736
1296 is a perfect square and divides 20736
2304 is a perfect square and divides 20736
5184 is a perfect square and divides 20736
20736 is a perfect square and divides 20736
Step 3: Divide To Perfect Square
Divide 20736 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 20736 in its simplest form: 144√1
How do you simplify √20736
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 20736. Divide 20736 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 144√1.
Simplified Decimal Form of √20736
The square root of 20736 is approximately 144 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √44 | 2√11 | √2 x √2 x √11 |
| √61 | Square root of 61 is the simplest radical form. | √61 |
| √51 | Square root of 51 is the simplest radical form. | √3 x √17 |
| √106 | Square root of 106 is the simplest radical form. | √2 x √53 |
| √231 | Square root of 231 is the simplest radical form. | √3 x √7 x √11 |
| √655 | Square root of 655 is the simplest radical form. | √5 x √131 |
| √6278 | Square root of 6278 is the simplest radical form. | √2 x √43 x √73 |
| √8793 | 3√977 | √3 x √3 x √977 |
| √8217 | 3√913 | √3 x √3 x √11 x √83 |