Square Root Of 1048576 In Simplest Radical Form
Simplify the square root of 1048576 to its lowest radical form.ANSWER: 1024√1
1024√1 is in the lowest radical form.
Simplified Radical Form of √1048576
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 √1048576, we need to divide into factors.
√1048576 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2Step 2: List Perfect Squares
1 is a perfect square and divides 1048576
4 is a perfect square and divides 1048576
16 is a perfect square and divides 1048576
64 is a perfect square and divides 1048576
256 is a perfect square and divides 1048576
1024 is a perfect square and divides 1048576
4096 is a perfect square and divides 1048576
16384 is a perfect square and divides 1048576
65536 is a perfect square and divides 1048576
262144 is a perfect square and divides 1048576
1048576 is a perfect square and divides 1048576
Step 3: Divide To Perfect Square
Divide 1048576 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 1048576 in its simplest form: 1024√1
How do you simplify √1048576
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 1048576. Divide 1048576 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 1024√1.
Simplified Decimal Form of √1048576
The square root of 1048576 is approximately 1024 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √98 | 7√2 | √2 x √7 x √7 |
| √77 | Square root of 77 is the simplest radical form. | √7 x √11 |
| √40 | 2√10 | √2 x √2 x √2 x √5 |
| √980 | 14√5 | √2 x √2 x √5 x √7 x √7 |
| √533 | Square root of 533 is the simplest radical form. | √13 x √41 |
| √910 | Square root of 910 is the simplest radical form. | √2 x √5 x √7 x √13 |
| √8226 | 3√914 | √2 x √3 x √3 x √457 |
| √1270 | Square root of 1270 is the simplest radical form. | √2 x √5 x √127 |
| √6772 | 2√1693 | √2 x √2 x √1693 |