Square Root Of 3952 In Simplest Radical Form
Simplify the square root of 3952 to its lowest radical form.ANSWER: 4√247
4√247 is in the lowest radical form.
Simplified Radical Form of √3952
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 √3952, we need to divide into factors.
√3952 = √2 x √2 x √2 x √2 x √13 x √19Step 2: List Perfect Squares
1 is a perfect square and divides 3952
4 is a perfect square and divides 3952
16 is a perfect square and divides 3952
Step 3: Divide To Perfect Square
Divide 3952 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 3952 in its simplest form: 4√247
How do you simplify √3952
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 3952. Divide 3952 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√247.
Simplified Decimal Form of √3952
The square root of 3952 is approximately 62.865 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √57 | Square root of 57 is the simplest radical form. | √3 x √19 |
| √54 | 3√6 | √2 x √3 x √3 x √3 |
| √77 | Square root of 77 is the simplest radical form. | √7 x √11 |
| √678 | Square root of 678 is the simplest radical form. | √2 x √3 x √113 |
| √282 | Square root of 282 is the simplest radical form. | √2 x √3 x √47 |
| √658 | Square root of 658 is the simplest radical form. | √2 x √7 x √47 |
| √7776 | 36√6 | √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √3 |
| √2630 | Square root of 2630 is the simplest radical form. | √2 x √5 x √263 |
| √8097 | Square root of 8097 is the simplest radical form. | √3 x √2699 |