Square Root Of 8712 In Simplest Radical Form
Simplify the square root of 8712 to its lowest radical form.ANSWER: 66√2
66√2 is in the lowest radical form.
Simplified Radical Form of √8712
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 √8712, we need to divide into factors.
√8712 = √2 x √2 x √2 x √3 x √3 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 8712
4 is a perfect square and divides 8712
9 is a perfect square and divides 8712
36 is a perfect square and divides 8712
121 is a perfect square and divides 8712
484 is a perfect square and divides 8712
1089 is a perfect square and divides 8712
4356 is a perfect square and divides 8712
Step 3: Divide To Perfect Square
Divide 8712 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 8712 in its simplest form: 66√2
How do you simplify √8712
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 8712. Divide 8712 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 66√2.
Simplified Decimal Form of √8712
The square root of 8712 is approximately 93.338 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √75 | 5√3 | √3 x √5 x √5 |
| √32 | 4√2 | √2 x √2 x √2 x √2 x √2 |
| √67 | Square root of 67 is the simplest radical form. | √67 |
| √664 | 2√166 | √2 x √2 x √2 x √83 |
| √782 | Square root of 782 is the simplest radical form. | √2 x √17 x √23 |
| √238 | Square root of 238 is the simplest radical form. | √2 x √7 x √17 |
| √8579 | Square root of 8579 is the simplest radical form. | √23 x √373 |
| √9487 | Square root of 9487 is the simplest radical form. | √53 x √179 |
| √6672 | 4√417 | √2 x √2 x √2 x √2 x √3 x √139 |