Square Root Of 140608 In Simplest Radical Form
Simplify the square root of 140608 to its lowest radical form.ANSWER: 104√13
104√13 is in the lowest radical form.
Simplified Radical Form of √140608
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 √140608, we need to divide into factors.
√140608 = √2 x √2 x √2 x √2 x √2 x √2 x √13 x √13 x √13Step 2: List Perfect Squares
1 is a perfect square and divides 140608
4 is a perfect square and divides 140608
16 is a perfect square and divides 140608
64 is a perfect square and divides 140608
169 is a perfect square and divides 140608
676 is a perfect square and divides 140608
2704 is a perfect square and divides 140608
10816 is a perfect square and divides 140608
Step 3: Divide To Perfect Square
Divide 140608 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 140608 in its simplest form: 104√13
How do you simplify √140608
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 140608. Divide 140608 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 104√13.
Simplified Decimal Form of √140608
The square root of 140608 is approximately 374.977 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √32 | 4√2 | √2 x √2 x √2 x √2 x √2 |
| √25 | 5√1 | √5 x √5 |
| √57 | Square root of 57 is the simplest radical form. | √3 x √19 |
| √446 | Square root of 446 is the simplest radical form. | √2 x √223 |
| √428 | 2√107 | √2 x √2 x √107 |
| √959 | Square root of 959 is the simplest radical form. | √7 x √137 |
| √2561 | Square root of 2561 is the simplest radical form. | √13 x √197 |
| √4305 | Square root of 4305 is the simplest radical form. | √3 x √5 x √7 x √41 |
| √4349 | Square root of 4349 is the simplest radical form. | √4349 |