Square Root Of 8144 In Simplest Radical Form
Simplify the square root of 8144 to its lowest radical form.ANSWER: 4√509
4√509 is in the lowest radical form.
Simplified Radical Form of √8144
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 √8144, we need to divide into factors.
√8144 = √2 x √2 x √2 x √2 x √509Step 2: List Perfect Squares
1 is a perfect square and divides 8144
4 is a perfect square and divides 8144
16 is a perfect square and divides 8144
Step 3: Divide To Perfect Square
Divide 8144 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 8144 in its simplest form: 4√509
How do you simplify √8144
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 8144. Divide 8144 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 4√509.
Simplified Decimal Form of √8144
The square root of 8144 is approximately 90.244 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √26 | Square root of 26 is the simplest radical form. | √2 x √13 |
| √57 | Square root of 57 is the simplest radical form. | √3 x √19 |
| √93 | Square root of 93 is the simplest radical form. | √3 x √31 |
| √134 | Square root of 134 is the simplest radical form. | √2 x √67 |
| √769 | Square root of 769 is the simplest radical form. | √769 |
| √354 | Square root of 354 is the simplest radical form. | √2 x √3 x √59 |
| √9102 | Square root of 9102 is the simplest radical form. | √2 x √3 x √37 x √41 |
| √7565 | Square root of 7565 is the simplest radical form. | √5 x √17 x √89 |
| √8213 | Square root of 8213 is the simplest radical form. | √43 x √191 |