Square Root Of 21381376 In Simplest Radical Form
Simplify the square root of 21381376 to its lowest radical form.ANSWER: 4624√1
4624√1 is in the lowest radical form.
Simplified Radical Form of √21381376
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 √21381376, we need to divide into factors.
√21381376 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √17 x √17 x √17 x √17Step 2: List Perfect Squares
1 is a perfect square and divides 21381376
4 is a perfect square and divides 21381376
16 is a perfect square and divides 21381376
64 is a perfect square and divides 21381376
256 is a perfect square and divides 21381376
289 is a perfect square and divides 21381376
1156 is a perfect square and divides 21381376
4624 is a perfect square and divides 21381376
18496 is a perfect square and divides 21381376
73984 is a perfect square and divides 21381376
83521 is a perfect square and divides 21381376
334084 is a perfect square and divides 21381376
1336336 is a perfect square and divides 21381376
5345344 is a perfect square and divides 21381376
21381376 is a perfect square and divides 21381376
Step 3: Divide To Perfect Square
Divide 21381376 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 21381376 in its simplest form: 4624√1
How do you simplify √21381376
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 21381376. Divide 21381376 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 4624√1.
Simplified Decimal Form of √21381376
The square root of 21381376 is approximately 4624 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √58 | Square root of 58 is the simplest radical form. | √2 x √29 |
| √27 | 3√3 | √3 x √3 x √3 |
| √63 | 3√7 | √3 x √3 x √7 |
| √423 | 3√47 | √3 x √3 x √47 |
| √265 | Square root of 265 is the simplest radical form. | √5 x √53 |
| √109 | Square root of 109 is the simplest radical form. | √109 |
| √4331 | Square root of 4331 is the simplest radical form. | √61 x √71 |
| √7688 | 62√2 | √2 x √2 x √2 x √31 x √31 |
| √9551 | Square root of 9551 is the simplest radical form. | √9551 |